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%I #15 Jun 24 2017 04:47:56
%S 1,-40,840,-12320,141640,-1358448,11297440,-83631680,561539400,
%T -3468363400,19922193200,-107343635040,546373245600,-2642351627440,
%U 12200693947200,-54007656632000,230002160331080,-945228781171920
%N Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-20).
%H Seiichi Manyama, <a href="/A004421/b004421.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 = 20 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015
%t nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^20, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)
%t nmax = 30; CoefficientList[Series[EllipticTheta[3, 0, x]^(-20), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 24 2017 *)
%K sign
%O 0,2
%A _N. J. A. Sloane_
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