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

1, -36, 684, -9120, 95724, -841320, 6433248, -43918272, 272670444, -1561033348, 8329222584, -41772509280, 198265106400, -895619289384, 3868763174208, -16044584545344, 64103055405804, -247461482137032

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

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

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^18, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)

Crossrefs

Sequence in context: A239181 A053947 A157092 * A268900 A185491 A220758

Adjacent sequences: A004416 A004417 A004418 * A004420 A004421 A004422

Keyword

sign

Author

N. J. A. Sloane

Status

approved