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%I #18 Jun 11 2017 02:37:51
%S 1,-48,1200,-20800,280752,-3142560,30338880,-259459200,2003790000,
%T -14178640368,92960115360,-569803615680,3289122824000,-17987650183200,
%U 93669997008000,-466466351287680,2229627536828592,-10261752523778400
%N Expansion of (Sum x^(n^2), n = -inf .. inf )^(-24).
%C From _Vaclav Kotesovec_, Aug 18 2015, extended Jan 16 2017: (Start)
%C In general, if g.f. = Product_{k>=1} ((1+x^k)/(1-x^k))^m and m>=1, then a(n) ~ exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)) * (1 - (m+3)*(m+1)/(8*Pi*sqrt(m*n))).
%C If g.f. = Product_{k>=1} ((1+(-x)^k)/(1-(-x)^k))^m and m>=1, then a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)) * (1 - (m+3)*(m+1)/(8*Pi*sqrt(m*n))).
%C (End)
%H Seiichi Manyama, <a href="/A004425/b004425.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 24 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015
%t nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^24, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)
%K sign
%O 0,2
%A _N. J. A. Sloane_
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