Re: A pigeonhole principle problem

From: John (halfsearch_at_hotmail.com)
Date: 12/06/04 

Date: 5 Dec 2004 19:58:32 -0800

"Ignacio Larrosa Caņestro" <ilarrosaQUITARMAYUSCULAS@mundo-r.com> wrote in message news:<31ha4eF3cbri7U1@individual.net>...
> S(x) = (1 + x + x^2 + ....)^14 = (Sum(x^k, k, 0, inf))^14 = 1/(1-x)^14
>
> But
>
> S(x) = d^13(1/(1-x))/dx^13 = Sum(Comb(13+k, k)x^k, k, 0, inf)
>
> and the coefficients are all > 0.

I know the value of the coefficient of x^k is the number of ways to
pick k objects, but I can't figure out how to use it in this problem.

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