A004409 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-8).
1, -16, 144, -960, 5264, -25056, 106944, -418176, 1520784, -5201232, 16871648, -52252992, 155341248, -445226848, 1234726272, -3323392128, 8704504976, -22234655520, 55498917840, -135595345600, 324759439584
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^8, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *) -
PARI
q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^8) \\ Altug Alkan, Sep 20 2018
Formula
a(n) ~ (-1)^n * exp(2*Pi*sqrt(2*n)) / (64*2^(3/4)*n^(11/4)). - Vaclav Kotesovec, Aug 18 2015
From Ilya Gutkovskiy, Sep 20 2018: (Start)
G.f.: 1/theta_3(x)^8, where theta_3() is the Jacobi theta function.
G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^8. (End)