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{{short description|Function that interpolates the factorial}} ...rawn through those points. Such a curve, namely one which interpolates the factorial but is not equal to the gamma function, is known as a pseudogamma function. ...

{{short description|Mathematical result on arithmetic properties of binomial coefficients}} ...)&nbsp;=&nbsp;5) equals the greatest common divisor of the second, fourth, and sixth of them (gcd(10,&nbsp;35,&nbsp;15)&nbsp;=&nbsp;5). --> <!-- That's a ...

{{short description|Identity involving binomial coefficients, first established by Zhi-Wei Sun in 2002}} ...entity''' is the following [[Identity (mathematics)|identity]] involving [[binomial coefficient]]s, first established by [[Zhi-Wei Sun]] in 2002: ...

...on methods have been studied.<ref>Shah S.M. (1971) "The displaced negative binomial distribution", ''Bulletin of the Calcutta Statistical Association'', 20, 14 ...istribution appeared in its general form in a paper by K. Hess, A. Liewald and K.D. Schmidt<ref name="Schmidt">{{cite journal ...

| name = Beta Negative Binomial ...^{(r)} = \frac{\Gamma(x+r)}{\Gamma(x)}</math> is the [[Pochhammer symbol]] and <math>{}_{2}F_{1}</math> is the [[hypergeometric function]]. ...

In [[mathematics]], the '''Fibonomial coefficients''' or '''Fibonacci-binomial coefficients''' are defined as ...&nbsp;≤&nbsp;''n'', ''F_j'' is the ''j''-th [[Fibonacci number]] and ''n''!_F is the ''n''th [[Fibonorial]], i.e. ...

...Springer-Verlag]]|year=1994|isbn=978-0387208602|location=|pages=79|chapter=Factorial n as the Product of n Large Factors}}</ref> ...ath display="inline">n!</math> grows with <math display="inline">n</math>, and is given by the sequence ...

{{short description|Array of partial sums of the binomial coefficients}} ...any integer ''k'' included between 0 and ''n'', the component in row ''n'' and column ''k'' is given by: ...

...of the largest power of a [[Prime number|prime]] ''p'' that divides the [[factorial]]&nbsp;''n''<nowiki>!</nowiki>. It is named after [[Adrien-Marie Legendre] For any prime number ''p'' and any positive integer ''n'', let <math>\nu_p(n)</math> be the exponent of th ...

...,''n''</sub> counts the ways that ''n''&nbsp;+&nbsp;''m'' open parentheses and ''n''&nbsp;−&nbsp;''m'' close parentheses can be arranged to form the start ...up>th</sup> Lobb number ''L''_''m'',''n'' is given in terms of [[binomial coefficient]]s by the formula ...

{{Short description|Generalization of the mathematical factorial}} ...'' !_{<math>\mathbb{Z}</math>}, would turn out to be the ordinary factorial of ''k''.<ref name=MAA>{{cite journal ...

...ort description|On finite sums of products of three binomial coefficients, and a hypergeometric sum}} ...]. These identities famously follow from the [[MacMahon Master theorem]], and can now be routinely proved by computer algorithms {{harv|Ekhad|1990}}. ...

...t vertex, 2 ways of permuting the two children of the upper middle vertex, and 5! = 120 ways of permuting the five children of the upper right vertex, for ...rphism group]] of a tree. These numbers are named after [[Camille Jordan]] and [[George Pólya]], who both wrote about them in the context of symmetries of ...

...ribution, samples are drawn until <math>r</math> failures have been found, and the distribution describes the probability of finding <math>k</math> succes ...math>N</math> elements, of which <math>K</math> are defined as "successes" and the rest are "failures". ...

...negative multinomial distribution''' is a generalization of the [[negative binomial distribution]] (NB(''x''₀,&thinsp;''p'')) to more than two outco ...ub>+...+''X''_''m'' is not fixed, being a draw from a [[negative binomial distribution]]. ...

...spective. For instance, the integrand is usually a [[rational function]], and the sum of the residues of a rational function is zero, yielding a new expr * First binomial coefficient integral ...

...h>n</math>-th row are indexed starting with <math>-n</math> from the left, and the middle entry has index 0. The symmetry of the entries of a row about th where <math>{n\choose k}_2=0</math> for <math>\ k<-n</math> and <math>\ k>n</math>. ...

{{Short description|Recurrence relations of binomial coefficients in Pascal's triangle}} ...ick identity''',<ref>CH Jones (1996) ''Generalized Hockey Stick Identities and N-Dimensional Block Walking.'' [[Fibonacci Quarterly]] '''34'''(3), 280-288 ...

==Definition and applications== ...iver starts looking for a space after already passing the only free space, and will be unable to park.{{r|riordan}} ...

In 1693 [[Samuel Pepys]] and [[Isaac Newton]] corresponded over a problem posed to Pepys by a school tea :A. Six fair dice are tossed independently and at least one "6" appears. ...