A022604 - OEIS

%I #17 Feb 06 2018 15:14:03

%S 1,-9,36,-93,207,-459,957,-1827,3357,-6061,10620,-18045,30006,-49122,

%T 79128,-125247,195435,-301599,460167,-694026,1036368,-1534305,2252277,

%U -3278709,4736973,-6797196,9689103,-13722487

%N Expansion of Product_{m>=1} (1+q^m)^(-9).

%H Seiichi Manyama, <a href="/A022604/b022604.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(0) = 1, a(n) = -(9/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 05 2017

%F G.f.: exp(-9*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 06 2018

%t nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^9, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%Y Column k=9 of A286352.

%K sign

%O 0,2

%A _N. J. A. Sloane_