4 issue 8607 ref ISIS 3 The Third International Study of Infarct Survival ISIS 3 was a 3 2 factorial experiment factorial trial that compared the three thrombolytic drugs streptokinase , tissue plasminogen ... D issue 8796 ref ISIS 4 The Fourth International Study of Infarct Survival ISIS 4 was a 2 2 2 factorial experiment factorial placebo controlled trial of the angiotensin converting enzyme inhibitor ... of Infarct Survival Collaborative Group year 1995 title ISIS 4 A randomised factorial trial assessing ... more details
Christian Kramp July 8, 1760 May 13, 1826 was a France French mathematician , who worked primarily with factorial s. Christian Kramp s father was his teacher at grammar school in Strasbourg . Kramp studied medicine and graduated, however, his interests certainly ranged outside medicine for, in addition to a number of medical publications, he published a work on crystallography in 1793. In 1795 France annexed the Rhineland area in which medical Kramp was carrying out his work and after this he became a teacher at Cologne this city was French from 1794 to 1815 , teaching mathematics, chemistry and physics. Kramp was appointed professor of mathematics at Strasbourg, the town of his birth, in 1809. He was elected to the geometry section of the French Academy of Sciences in 1817. As Friedrich Bessel Bessel , Adrien Marie Legendre Legendre and Carl Friedrich Gauss Gauss did, Kramp worked on the generalised factorial function which applied to non integers. His work on factorials is independent of that of James Stirling mathematician James Stirling and Vandermonde . He was the first to use the notation n Elements d arithm tique universelle , 1808 . In fact, the more general concept of factorial was found at the same time by Antoine Arbogast Arbogast . External links http members.aol.com jeff570 stat.html Portions of Elements d arithm tique universelle MacTutor Biography id Kramp Persondata Metadata see Wikipedia Persondata . NAME Kramp, Christian ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH July 8, 1760 PLACE OF BIRTH DATE OF DEATH May 13, 1826 PLACE OF DEATH DEFAULTSORT Kramp, Christian Category 1760 births Category 1826 deaths Category 19th century mathematicians Category French mathematicians France mathematician stub cs Christian Kramp de Christian Kramp eo Christian Kramp fr Christian Kramp io Christian Kramp ht Christian Kramp pl Christian Kramp ru , sk Christian Kramp vi Christian Kramp zh ... more details
otheruses2 Babbage notability date October 2011 primary sources date October 2011 Infobox programming language name Babbage logo paradigm procedural programming procedural , structured programming structured , High level assembler year around 1971 designer developer latest release version 308 latest release date latest test version latest test date typing implementations dialects influenced by BCPL influenced operating system COS, GEC DOS, OS4000 license website Babbage is the High level assembler high level assembly language for the GEC 4000 series minicomputers . ref cite book last Salomon first David others title Assemblers and Loaders year 1992 publisher Ellis Horwood isbn 0130525642 pages 184 185 url http www.scribd.com doc 7326575 Assembly Language ref It was named after Charles Babbage , an English people English computing pioneer. Example pre PROCESS CHAPTER FACTORIAL ENTRY LABEL ENTRYPOINT LITERAL TO 4 Assume using the default proforma EXTERNAL ROUTINE OPEN, PUT, CLOSE, TOCHAR VECTOR 0,19 OF BYTE ANSWER factorial x xxxxxx HALF COUNT HALF VALUE FULL RESULT ROUTINE FACT VALUE return factorial of RA. VALUE RESULT WHILE DECREMENT VALUE GT 0 DO RESULT VALUE RESULT RETURN RESULT END ENTRYPOINT OPEN TO, 1 Print factorials for numbers 1 through 9 1 RA REPEAT RA COUNT FACT RA RA TOCHAR RA, 7, ANSWER 13 TOCHAR COUNT, 2, ANSWER 9 PUT TO, 20, ANSWER COUNT 1 RA WHILE RA LT 10 CLOSE TO STOP 0 END pre See also GEC 4000 series OS4000 References reflist Category Articles with example code Category Systems programming languages Category Assembly languages Category Assemblers Category Charles Babbage Category General Electric Company computer products compu lang stub ... more details
Notability date December 2009 In mathematics , the Fibonorial n sub F sub , also called the Fibonacci factorial , where n is a non negative integer, is defined as the product of the first n nonzero Fibonacci numbers math n F F n F n 1 cdots F 1 text and 0 F 1, math where F sub i sub is the i th Fibonacci number. 0 sub F sub is 1 since it is the empty product. The Fibonorial of n n sub F sub is defined analogously to the factorial of n i.e. to n nowiki nowiki . The Fibonorial numbers are used in the definition of Fibonomial coefficient s or Fibonacci binomial coefficients similarly as the factorial numbers are used in the definition of binomial coefficients . It is interesting to look for prime numbers among the almost Fibonorial numbers n sub F sub &minus 1 and the quasi Fibonorial numbers n sub F sub 1 . Cf. OEIS http www.research.att.com njas sequences A003266 A003266 Product of first n nonzero Fibonacci numbers F 1 , ..., F n . Cf. OEIS http www.research.att.com njas sequences A059709 A059709 and http www.research.att.com njas sequences A053408 A053408 for n such that n sub F sub &minus 1 and n sub F sub 1 are primes. Cf. Eric W. Weisstein s MathWorld http mathworld.wolfram.com Fibonorial.html Fibonorial. References cite web url http mathworld.wolfram.com Fibonorial.html title Fibonorial first Eric W. last Weisstein work MathWorld publisher Wolfram Research accessdate 19 December 2009 Category Fibonacci numbers cs Fibonori l ... more details
Software that is used for designing factorial experiments plays an important role in scientific experiment s generally and represents a route to the implementation of design of experiments procedures that derive from statistics statistical and combinatorics combinatoric theory. In fact, in September 2009, at the International Industrial Statistics in Action Conference at Newcastle University in England, statisticians from SmithKline Beecham Pharmaceuticals put up a poster saying that easy to use design of experiments DOE software product name omitted here to maintain article neutrality must be made available to all experimenters to foster use of DOE. ref Marion Chatfield and Gillian Smith, SmithKline Beecham Pharmaceuticals, Experiences of Promoting the Use of Design of Experiments in Synthetic Chemistry. ref Background Main Design of experiments The term design of experiments DOE derives from early statistical work performed by Ronald Fisher Sir Ronald Fisher . He was described by Anders Hald as a genius who almost single handedly created the foundations for modern statistical science ... factorial design of experiments began ensuring that inferences and conclusions could profitably ... the extent to which a crop sample chosen was truly representative. Factorial DOE began revealing ... collection procedures trend estimation . Use of software Factorial experimental design software drastically ... World War II, a more sophisticated form of DOE, called factorial design, became a big weapon for speeding ... Page needed date September 2010 ref describe stronger multi factorial DOE methods as being more Robust ... rise to solving complex factorial statistical equations, statisticians began in earnest to design ... key factors for process or product improvements. Setting up and analyzing Factorial experiment general factorial , two level factorial, Fractional factorial design fractional factoria up to 31 ... factor settings for multiple responses simultaneously. Today, factorial DOE software is a notable ... more details
In mathematics , a polynomial sequence is a sequence of polynomial s indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial. Polynomial sequences are a topic of interest in enumerative combinatorics and algebraic combinatorics , as well as applied mathematics . Examples Some polynomial sequences arise in physics and approximation theory as the solutions of certain ordinary differential equation s Laguerre polynomials Chebyshev polynomials Legendre polynomials Jacobi polynomials Others come from statistics Hermite polynomials Many are studied in algebra and combinatorics Monomial s Rising factorial s Falling factorial s Abel polynomials Bell polynomials Bernoulli polynomials Dickson polynomial s Fibonacci polynomials Lagrange polynomials Lucas polynomials Spread polynomials Touchard polynomials Rook polynomials Classes of polynomial sequences Polynomial sequences of binomial type Orthogonal polynomials Secondary polynomials Sheffer sequence Sturm sequence Generalized Appell polynomials See also Umbral calculus References Aigner, Martin. A course in enumeration , GTM Springer, 2007, ISBN 3 540 39032 4 p21. Roman, Steven The Umbral Calculus , Dover Publications, 2005, ISBN 0 486 44129 3 Please check ISBN reason Check digit 3 does not correspond to calculated figure. . Williamson, S. Gill Combinatorics for Computer Science , Dover Publications, 2002 p177. DEFAULTSORT Polynomial Sequence Category Polynomials Category Sequences and series ar fr Suite de polyn mes it Sequenza polinomiale ... more details
File Star of david thm.jpg thumb 250px The Star of David theorem the rows of the Pascal triangle are shown as columns here . The Star of David theorem is a mathematical result on arithmetic properties of binomial coefficients . It was discovered by H.W. Gould in 1972. Statement The greatest common divisor s of binomial coefficients forming the Star of David shape in Pascal s triangle , are equal math begin align & quad gcd left binom n 1 k 1 , binom n k 1 , binom n 1 k right 8pt & gcd left binom n 1 k , binom n k 1 , binom n 1 k 1 right . end align math See also List of factorial and binomial topics References H.W. Gould, A New Greatest Common Divisor Property of The Binomial Coefficients, Fibonacci Quarterly 10 1972 , 579&ndash 584. http mathforum.org wagon fall07 p1088.html Star of David theorem , from MathForum . http threesixty360.wordpress.com 2008 12 21 star of david theorem Star of David theorem , blog post. External links http mathworld.wolfram.com StarofDavidTheorem.html Star of David theorem , from MathWorld . http demonstrations.wolfram.com StarOfDavidTheorem Demonstration of the Star of David theorem , in Mathematica . Category Theorems in discrete mathematics Category Combinatorics Category Factorial and binomial topics ... more details
means can be illustrated with an example of a factorial function, which in non template C can be written using recursion as follows source lang cpp constexpr unsigned int factorial unsigned int n return n 0 ? 1 n factorial n 1 const int x factorial 4 4 3 2 1 1 24 const int y factorial 0 0 1 source The code above will execute at run time to determine the factorial value of the literals 4 and 0. By using ..., the factorials used in the program, ignoring any factorial not used, can be calculated at compile time by this code source lang cpp template int N struct Factorial enum value N Factorial N 1 value template struct Factorial 0 enum value 1 Factorial 4 value 24 Factorial 0 value 1 const int x Factorial 4 value 24 const int y Factorial 0 value 1 source The code above calculates the factorial ... at compile time, which has the natural precondition that code Factorial code X code value code ... expression. Compile time code optimization The factorial example above is one example of compile ... more details
A binomial is a polynomial with two terms. Binomial may also refer to In mathematics Binomial theorem , a theorem about powers of binomials Binomial coefficient , numbers appearing in the expansions of powers of binomials Binomial type , a property of sequences of polynomials In probability and statistics Binomial distribution , a type of probability distribution Binomial test , a test of significance In computing science Binomial heap , a data structure In linguistics Binomial pair In biology A binomial nomenclature binomial name, a two term name for a species, such as Sequoia sempervirens In finance Binomial options pricing model See also List of factorial and binomial topics Disambig de Binomial es Binomial desambiguaci n fr Bin me ... more details
The one factor at a time method or OFAT is a method of design of experiments designing experiments involving the testing of factors, or causes, one at a time instead of all simultaneously. Prominent text books and academic papers currently favor factorial design factorial experimental designs , a method pioneered by Ronald Fisher Sir Ronald A. Fisher , where multiple factors are changed at once. The reasons stated for favoring the use of factorial design over OFAT are 1. OFAT requires more runs for the same precision in effect estimation br 2. OFAT cannot estimate interactions br 3. OFAT can miss optimal settings of factors Despite these criticisms, some researchers have articulated a role for OFAT and showed they can be more effective than Fractional factorial design fractional factorials under certain conditions number of runs is limited, primary goal is to attain improvements in the system, and experimental error is not large compared to factor effects, which must be additive and independent of each other . ref name Friedman, M., and Savage, L. J. 1947 , Planning Experiments Seeking Maxima, in Techniques of Statistical Analysis, eds. C. Eisenhart, M. W. Hastay, and W. A. Wallis, New York McGraw Hill, pp. 365 372. Friedman, M., and Savage, L. J. 1947 , Planning Experiments Seeking Maxima, in Techniques of Statistical Analysis, eds. C. Eisenhart, M. W. Hastay, and W. A. Wallis, New York McGraw Hill, pp. 365 372. ref ref name Cuthbert Daniel Daniel , C. 1973 , One at a Time Plans, Journal of the American Statistical Association 68, 353 360 ref Designed experiments remain nearly always preferred to OFAT with many types and methods available, ref See Category Experimental design, at bottom. ref in addition to fractional factorials which, though usually requiring more runs than OFAT, do address the three concerns above. ref name Czitrom http www.questia.com googleScholar.qst?docId 5001888588 Czitrom 1999 One Factor at a Time Versus Designed Experiments , American Stati ... more details
List of factorial and binomial topics References Philippe Flajolet and Robert Sedgewick, http ... Finite differences Category Factorial and binomial topics Category Mathematics related lists Newton ... more details
Unreferenced date December 2006 In mathematics , the generalized Pochhammer symbol of parameter math alpha 0 math and partition number theory partition math kappa kappa 1, kappa 2, ldots, kappa m math generalizes the classical Pochhammer symbol , named after Leo August Pochhammer , and is defined as math a alpha kappa prod i 1 m prod j 1 kappa i left a frac i 1 alpha j 1 right . math DEFAULTSORT Generalized Pochhammer Symbol Category Gamma and related functions Category Factorial and binomial topics numtheory stub ... more details
. A simple Cool program for computing factorial follows pre class Main IO is Main begin out string ... Number must be greater than or equal to 0 n else out string The factorial of .out int input out string is .out int factorial input fi end end factorial num Integer Integer if num 0 then 1 else num factorial num 1 fi end pre The syntax used in this sample comes out of Cool 2008, a dialect of Cool ... more details
In combinatorics combinatorial mathematics , the Stirling transform of a sequence a sub n sub n 1, 2, 3, ... of numbers is the sequence b sub n sub n 1, 2, 3, ... given by math b n sum k 1 n left begin matrix n k end matrix right a k, math where math left begin matrix n k end matrix right math is the Stirling number of the second kind, also denoted S n , k with a capital S , which is the number of partition of a set partitions of a set of size n into k parts. The inverse transform is math a n sum k 1 n s n,k b k, math where s n , k with a lower case s is a Stirling number of the first kind. Berstein and Sloane cited below state If a sub n sub is the number of objects in some class with points labeled 1, 2, ..., n with all labels distinct, i.e. ordinary labeled structures , then b sub n sub is the number of objects with points labeled 1, 2, ..., n with repetitions allowed . If math f x sum n 1 infty a n over n x n math is a formal power series note that the lower bound of summation is 1, not 0 , and math g x sum n 1 infty b n over n x n math with a sub n sub and b sub n sub as above, then math g x f e x 1 . , math See also Binomial transform List of factorial and binomial topics References M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers , Linear Algebra and Applications , 226 228 1995 , 57 72. Category Factorial and binomial topics Category Transforms ... more details
This is a list of topics on mathematical permutation s. Alternating group Alternating permutation Antisymmetrizer Automorphisms of the symmetric and alternating groups Bijection Bit reversal permutation Block permutation group theory Burnside ring Cayley s theorem Circular shift Claw free permutation Combination Costas array Cycle index Cycle mathematics Cycle notation Cycles and fixed points Cyclic order Cyclic permutation Derangement Direct sum of permutations Enumerations of specific permutation classes Even and odd permutations&mdash see Parity of a permutation Ewens sampling formula Factorial Falling factorial Faro shuffle Fifteen puzzle Fisher Yates shuffle Frobenius group Generalized permutation matrix Golomb Dickman constant Identical particles Inversion discrete mathematics Josephus permutation Jucys Murphy element Landau s function Levi Civita symbol Major index M nage problem Method ringing Oligomorphic group Order statistic Parity of a permutation Parker vector Permutable prime Permutation Permutation automaton Permutation cipher Permutation music Permutation graph Permutation group Permutation matrix Generalized permutation matrix Permutation pattern Permutation polynomial Permutohedron Primitive permutation group Random permutation Random permutation statistics Rank 3 permutation group Rankit Representation theory of the symmetric group Rencontres numbers Resampling statistics Robinson Schensted correspondence Schreier vector Separable permutation Shuffling Skew sum of permutations Sorting algorithm Sorting network Stanley Wilf conjecture Steinhaus Johnson Trotter algorithm Strong generating set Substitution cipher Substitution permutation network Sum of permutations Direct sum of permutations Skew sum of permutations Superpattern Symmetric function Symmetric group Symmetric inverse semigroup Szymanski s conjecture Transposition cipher Transposition mathematics Twelvefold way Unpredictable permutation Weak order of permutations Wreath product Young sym ... more details
A Pillai prime is a prime number p for which there is an integer n 0 such that the factorial of n is one less than a multiple of the prime, but the prime is not one more than a multiple of n . To put it algebraically, math n equiv 1 mod p math but math p not equiv 1 mod n math . The first few Pillai primes are 23 number 23 , 29 number 29 , 59 number 59 , 61 number 61 , 67 number 67 , 71 number 71 , 79 number 79 , 83 number 83 , 109 number 109 , 137 number 137 , 139 number 139 , 149 number 149 , 193 number 193 , ... OEIS id A063980 Pillai primes are named after the mathematician Subbayya Sivasankaranarayana Pillai , who asked about these numbers. Their infinitude has been proved several times, by Subbarao, Erd s, and Hardy & Subbarao. References Citation first R. K. last Guy title Unsolved Problems in Number Theory location New York publisher Springer Verlag year 2004 page A2 edition 3rd isbn 0387208607 . Citation first G. E. last Hardy lastauthoramp yes first2 M. V. last2 Subbarao title A modified problem of Pillai and some related questions journal American Mathematical Monthly volume 109 issue 6 year 2002 pages 554 559 doi 10.2307 2695445 . planetmath reference id 8739 title Pillai prime Prime number classes Category Classes of prime numbers Category Factorial and binomial topics numtheory stub es N mero primo de Pillai pt N mero primo de Pillai ta ... more details
this one can define the q analog of the factorial , the q factorial , as math big n q math math prod ... n . math Again, one recovers the usual factorial by taking the limit as q approaches 1. This can be interpreted ... brackets can be expressed in terms of the q factorial as math prod k 1 n k q frac 1 n , n q q n n 1 ... of the q factorial function to the real number system. See also Basic hypergeometric series Pochhammer ... q Analog title q Analog MathWorld urlname q Bracket title q Bracket MathWorld urlname q Factorial title q Factorial MathWorld urlname q BinomialCoefficient title q Binomial Coefficient Category Number ... more details
In the mathematical theory of special functions , the Pochhammer k symbol and the k gamma function , introduced by Rafael D az and Eddy Pariguan ref cite arxiv date 2005 class math.CA eprint math 0405596 first Rafael last D az coauthors Eddy Pariguan title On hypergeometric functions and k Pochhammer symbol ref , are generalizations of the Pochhammer symbol and gamma function . They differ from the Pochhammer symbol and gamma function in that they can be related to a general arithmetic progression in the same manner as those are related to the sequence of consecutive integer s. The Pochhammer k symbol x sub n,k sub is defined as math x n,k x x k x 2k cdots x n 1 k , , math and the k gamma function sub k sub , with k 0, is defined as math Gamma k x lim n to infty frac n k n nk x k 1 x n,k . math When k 1 the standard Pochhammer symbol and gamma function are obtained. D az and Pariguan use these definitions to demonstrate a number of properties of the hypergeometric function . Although D az and Pariguan restrict these symbols to k 0, the Pochhammer k symbol as they define it is well defined for all real k, and for negative k gives the falling factorial , while for k 0 it reduces to the Exponentiation power x sup n sup . The D az and Pariguan paper does not address the many analogies between the Pochhammer k symbol and the power function, such as the fact that the binomial theorem can be extended to Pochhammer k symbols. It is true, however, that many equations involving the power function x sup n sup continue to hold when x sup n sup is replaced by x sub n,k sub . References references Category Gamma and related functions Category Factorial and binomial topics sl Pochhammerjev k simbol ... more details
Full and fractional factorial design s are common in designed experiment s for engineering and scientific applications. In these designs, each factor is assigned two levels. These are typically called the low and high levels. For computational purposes, the factors are scaled so that the low level is assigned a value of 1 and the high level is assigned a value of 1. These are also commonly referred to as and . A full factorial design contains all possible combinations of low high levels for all the factors. A fractional factorial design contains a carefully chosen subset of these combinations. The criterion for choosing the subsets is discussed in detail in the fractional factorial designs article. Formalized by Frank Yates , a Yates analysis exploits the special structure of these designs to generate least squares estimates for factor effects for all factors and all relevant interactions. The Yates analysis can be used to answer the following questions What is the ranked list of factors? What is the goodness of fit as measured by the residual standard deviation for the various models? The mathematical details of the Yates analysis are given in chapter 10 of Box, Hunter, and Hunter 1978 . The Yates analysis is typically complemented by a number of graphical technique s such as the dex mean plot and the dex contour plot dex stands for design of experiments . Yates order Before performing a Yates analysis, the data should be arranged in Yates order . That is, given k factors, the k sup th sup column consists of 2 sup k 1 sup minus signs i.e., the low level of the factor followed by 2 sup k 1 sup plus signs i.e., the high level of the factor . For example, for a full factorial ... math math math math math math Determining the Yates order for fractional factorial designs requires knowledge of the confounding structure of the fractional factorial design. Output A Yates analysis generates .... This is not the case when the design is orthogonal, as is a 2 sup 3 sup full factorial design ... more details
In computing, Recursion termination is when certain conditions are met and the recursive algorithm ceases calling itself and begins to return values. ref http www.itl.nist.gov div897 sqg dads HTML recursiontrm.html ref This happens only if with every recursive call the recursive algorithm changes its state and moves towards the base case. Cases that satisfy the definition without being defined in terms of the definition itself are called base cases. They are small enough to solve directly. ref cite book title Recursion Lecture, Introduction to Computer Science pg. 3 url http www.cdf.toronto.edu csc148h winter stg lectures w3 1 m Recursion.pdf ref Examples Fibonacci function The Fibonacci function fibonacci n , which takes integer n n 0 as input, has three conditions 1. if n is 0, returns 0. br 2. if n is 1, returns 1. br 3. otherwise, return fibonacci n 1 fibonacci n 2 This recursive function terminates if either conditions 1 or 2 are satisfied. We see that the function s recursive call reduces the value of n by passing n 1 or n 2 in the function ensuring that n reaches either condition 1 or 2. C C Example ref cite book title An Introduction to the Imperative Part of C url http www.doc.ic.ac.uk wjk C Intro RobMillerL8.html ref pre int factorial int number else if number 0 return 1 else return number factorial number 1 pre Here we see that in the recursive call, the number passed in the recursive step is reduced by 1. This again ensures that the number will at some point reduce to 0 which in turn terminates the recursive algorithm. References reflist 2 External links http www.cs.princeton.edu courses archive spr05 cos126 lectures 07.pdf Princeton university An introduction to computer science in the context of scientific, engineering, and commercial applications http www.cdf.toronto.edu csc148h winter stg lectures w3 1 m Recursion.pdf University of Toronto Introduction to Computer Science Category Computer programming Category Recursion compu prog stub ... more details
wiktionary exclamation mark exclamation point is a punctuation mark called an exclamation mark , exclamation point, ecphoneme, or bang. may also refer to tocright Mathematics and computers Factorial , a mathematical function Derangement , a related mathematical function Negation , in logic and some programming languages Uniqueness quantification in mathematics and logic Music album album , a 1995 album by The Dismemberment Plan Chk, chk, chk , an American dance punk band The Song Formerly Known As , a single on the album Unit album Unit by Regurgitator , an album by house music singer Adeva , an album by R&B gospel singer Shirley Murdock Other Unicode the IPA symbol for alveolar clicks postalveolar click in speech An indicator of a good chess move in Punctuation chess Good move punctuation A dereference operator in BCPL See also disambiguation Interrobang , the nonstandard mix of a question mark and an exclamation mark disambiguation es desambiguaci n ko it disambigua he ru zh ... more details
The Genocchi numbers , named after Angelo Genocchi , are a sequence mathematics sequence of integer s, G sub n sub that satisfy the relation math frac 2t e t 1 sum n 1 infty G n frac t n n . math The first few Genocchi numbers are 1, &minus 1, 0, 1, 0, &minus 3, 0, 17 OEIS id A001469 . G sub n sub is 0 for odd n 1. It has been proven that &minus 3 number 3 and 17 number 17 are the only prime number prime Genocchi numbers. They are related to Bernoulli numbers B sub n sub by the formula math G n 2 , 1 2 n ,B n. math References MathWorld urlname GenocchiNumber title Genocchi Number Category Integer sequences Category Factorial and binomial topics es N mero de Genocchi fr Nombre de Genocchi it Numeri di Genocchi nl Genocchigetal ... more details
Abel s binomial theorem , named after Niels Henrik Abel , states the following math sum k 0 m binom m k w m k m k 1 z k k w 1 z w m m. math Example m 2 math begin align & quad binom 2 0 w 2 1 z 0 0 binom 2 1 w 1 0 z 1 1 binom 2 2 w 0 1 z 2 2 & w 2 2 z 1 frac z 2 2 w & frac z w 2 2 w . end align math See also Binomial theorem Binomial type References mathworld title Abel s binomial theorem urlname AbelsBinomialTheorem Category Factorial and binomial topics Category Theorems in algebra fr Th or me binomial d Abel hu Abel binomi lis t tele km ru ta ... more details
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