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

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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)

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 *)

Prog

(PARI) q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^8) \\ Altug Alkan, Sep 20 2018

Crossrefs

Cf. A000122, A000143.

Sequence in context: A060300 A128985 A341369 * A319553 A054851 A000762

Adjacent sequences: A004406 A004407 A004408 * A004410 A004411 A004412

Keyword

sign

Author

N. J. A. Sloane

Status

approved