Re: what is coefficients of expanding (1+x+x^2+....+x^k)^n?
From: Phil Carmody (thefatphil_demunged_at_yahoo.co.uk)
Date: 07/06/04
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Date: 06 Jul 2004 19:01:40 +0300
zhora@univ.kiev-dot-ua.no-spam.invalid (zhora) writes:
> > L.P.wrote:
> The formulae is well known for k=2,3,4,5..-binomial, trinomial,
> > quadromial , hexanomial numbers..What is general fornulae for
> > arbitrary k???
> If you mean x^k "x to the power k", then the coefficient before x^j in
> your expansion is equal to the number of non-negative integer
> solutions to the equation j_1+...+j_k=j, the last number equals to
> the binomial coefficient ((k+j-1)c(k-1)).
That doesn't depend on n.
Phil
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