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A004404 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-3). 5
1, -6, 24, -80, 234, -624, 1552, -3648, 8184, -17654, 36816, -74544, 147056, -283440, 535008, -990912, 1803882, -3232224, 5707624, -9943536, 17106960, -29088352, 48922320, -81438528, 134261584, -219336630, 355242288 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..4000 from Robert Israel)

Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 8.

FORMULA

a(n) ~ (-1)^n * 3*exp(Pi*sqrt(3*n)) / (64*n^(3/2)) * (1 - sqrt(3)/(Pi*sqrt(n))). - Vaclav Kotesovec, Aug 18 2015, extended Jan 16 2017

MAPLE

S:= series(1/JacobiTheta3(0, x)^3, x, 101):

seq(coeff(S, x, j), j=0..100); # Robert Israel, Dec 29 2015

MATHEMATICA

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

CROSSREFS

Cf. A001934, A004405-A004425, A015128.

Sequence in context: A140088 A011855 A173031 * A319552 A201189 A001788

Adjacent sequences:  A004401 A004402 A004403 * A004405 A004406 A004407

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 20 12:05 EDT 2019. Contains 324234 sequences. (Running on oeis4.)