A004421 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-20).

1, -40, 840, -12320, 141640, -1358448, 11297440, -83631680, 561539400, -3468363400, 19922193200, -107343635040, 546373245600, -2642351627440, 12200693947200, -54007656632000, 230002160331080, -945228781171920

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 = 20 for this sequence. - Vaclav Kotesovec, Aug 18 2015

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^20, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)
nmax = 30; CoefficientList[Series[EllipticTheta[3, 0, x]^(-20), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 24 2017 *)

Crossrefs

Sequence in context: A162402 A010992 A250584 * A247411 A250986 A190825

Adjacent sequences: A004418 A004419 A004420 * A004422 A004423 A004424

Keyword

sign

Author

N. J. A. Sloane

Status

approved