|
%I #32 Oct 26 2023 00:19:51
%S 1,-6,24,-80,234,-624,1552,-3648,8184,-17654,36816,-74544,147056,
%T -283440,535008,-990912,1803882,-3232224,5707624,-9943536,17106960,
%U -29088352,48922320,-81438528,134261584,-219336630,355242288
%N Expansion of 1 / (Sum_{n=-oo..oo} x^(n^2))^3.
%H Seiichi Manyama, <a href="/A004404/b004404.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..4000 from Robert Israel)
%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 8.
%F 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
%p S:= series(1/JacobiTheta3(0,x)^3,x,101):
%p seq(coeff(S,x,j),j=0..100); # _Robert Israel_, Dec 29 2015
%t nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)
%Y Cf. A001934, A004405-A004425, A015128.
%K sign
%O 0,2
%A _N. J. A. Sloane_
|
