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A004421 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-20). 1
1, -40, 840, -12320, 141640, -1358448, 11297440, -83631680, 561539400, -3468363400, 19922193200, -107343635040, 546373245600, -2642351627440, 12200693947200, -54007656632000, 230002160331080, -945228781171920 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 17 19:58 EDT 2021. Contains 347489 sequences. (Running on oeis4.)