A004407 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-6).

1, -12, 84, -448, 2004, -7896, 28224, -93312, 289236, -848972, 2377704, -6391872, 16571968, -41599320, 101430144, -240877440, 558440916, -1266406680, 2814053908, -6136337088, 13148606184, -27717527552

Offset

0,2

Links

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

Formula

a(n) ~ (-1)^n * 3^(7/4)*exp(Pi*sqrt(6*n)) / (256*2^(3/4)*n^(9/4)). - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^6, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^6. (End)

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^6, {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)^6) \\ Altug Alkan, Sep 20 2018

Crossrefs

Cf. A000122, A000141.

Sequence in context: A303916 A111464 A341367 * A054849 A000761 A174079

Adjacent sequences: A004404 A004405 A004406 * A004408 A004409 A004410

Keyword

sign

Author

N. J. A. Sloane

Status

approved