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A004419 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-18). 1

%I #15 Jun 12 2017 05:02:06

%S 1,-36,684,-9120,95724,-841320,6433248,-43918272,272670444,

%T -1561033348,8329222584,-41772509280,198265106400,-895619289384,

%U 3868763174208,-16044584545344,64103055405804,-247461482137032

%N Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-18).

%H Seiichi Manyama, <a href="/A004419/b004419.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 = 18 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015

%t nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^18, {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 March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)