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A004420 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-19). 1

%I

%S 1,-38,760,-10640,117002,-1075248,8582224,-61061440,394559320,

%T -2348001494,13008061200,-67666510320,332809029680,-1556541579760,

%U 6955832361824,-29820933412800,123079426294922,-490508040685920

%N Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-19).

%H Seiichi Manyama, <a href="/A004420/b004420.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 = 19 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015

%t nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^19, {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 September 18 14:52 EDT 2021. Contains 347527 sequences. (Running on oeis4.)