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Expansion of Product_{m>=1} (1+q^m)^(-15).
3

%I #13 Apr 05 2017 09:50:16

%S 1,-15,105,-470,1590,-4593,12160,-30075,69780,-153750,325728,-667020,

%T 1323915,-2557140,4824630,-8912759,16148505,-28746945,50364835,

%U -86956260,148098384,-249060745,413975085,-680602545

%N Expansion of Product_{m>=1} (1+q^m)^(-15).

%C a(0) = 1, a(n) = -(15/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 05 2017

%H Seiichi Manyama, <a href="/A022610/b022610.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (-1)^n * 5^(1/4) * exp(Pi*sqrt(5*n/2)) / (2^(7/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^15, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_