extension of binomial coefficient (?)
in [Math]
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From: kj on 13 Jul 2010 13:10 In my derivations for some work I've been doing I keep coming across expressions of the form (n-x)!x! -------- (n-y)!y! where n, x, y are all integers such that n>=x,y>=0. The binomial coefficients make up a subset of these numbers, corresponding to the special case where x = 0. Is there a name for such numbers? TIA! ~K
From: Virgil on 13 Jul 2010 13:48
In article <i1i6ms$bhh$1(a)reader1.panix.com>, kj <no.email(a)please.post> wrote: > In my derivations for some work I've been doing I keep coming across > expressions of the form > > (n-x)!x! > -------- > (n-y)!y! > > where n, x, y are all integers such that n>=x,y>=0. > > The binomial coefficients make up a subset of these numbers, > corresponding to the special case where x = 0. > > Is there a name for such numbers? > > TIA! > > ~K What you have is also just the quotient of two binomial coefficients: (n-x)!x! / (n-y)!y! = Binomial(n,y) / Binomial(n,x). I suspect that there is no simpler name for such numbers. |