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find-the-coefficient-a-k-of-term-x-k-in-r-1-n-1-x-r-with-0-k-n-n-1-2-example-n-100-k-50-




Question Number 73224 by mr W last updated on 09/Nov/19
find the coefficient a_k  of term x^k  in  Π_(r=1) ^n (1+x^r ) with 0≤k≤((n(n+1))/2)    example: n=100, k=50
$${find}\:{the}\:{coefficient}\:{a}_{{k}} \:{of}\:{term}\:{x}^{{k}} \:{in} \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+{x}^{{r}} \right)\:{with}\:\mathrm{0}\leqslant{k}\leqslant\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$$$ \\ $$$${example}:\:{n}=\mathrm{100},\:{k}=\mathrm{50} \\ $$
Answered by mind is power last updated on 08/Nov/19
this π(n,k) ramanujan fonction of partition of an integer n in k integer
$$\mathrm{this}\:\pi\left(\mathrm{n},\mathrm{k}\right)\:\mathrm{ramanujan}\:\mathrm{fonction}\:\mathrm{of}\:\mathrm{partition}\:\mathrm{of}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{n}\:\mathrm{in}\:\mathrm{k}\:\mathrm{integer} \\ $$$$ \\ $$$$ \\ $$

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