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A004423 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-22). 1

%I

%S 1,-44,1012,-16192,202356,-2102936,18896064,-150747520,1088265332,

%T -7211641580,44356933544,-255472920256,1387689358528,-7151069205016,

%U 35134409940608,-165273439140480,747047401948276,-3254796172584792

%N Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-22).

%H Seiichi Manyama, <a href="/A004423/b004423.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 = 22 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015

%t nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^22, {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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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)