|
%I #12 Jan 02 2017 07:05:12
%S 1,-32,496,-4992,36984,-217280,1066432,-4548352,17369116,-60711456,
%T 197327712,-603261056,1749861312,-4849210560,12909347456,-33162318080,
%U 82507571334,-199432268416,469559849680,-1079335967872
%N Expansion of Product_{m>=1} (1+q^m)^(-32).
%C In general, for k > 0, if g.f. = Product_{m>=1} 1/(1+q^m)^k, then a(n) ~ (-1)^n * exp(Pi*sqrt(k*n/6)) * k^(1/4) / (2^(7/4) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 27 2015
%H Seiichi Manyama, <a href="/A022627/b022627.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ (-1)^n * exp(4*Pi*sqrt(n/3)) / (sqrt(2) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 27 2015
%t nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^32, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)
%K sign
%O 0,2
%A _N. J. A. Sloane_
|
