A004408 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-7).

1, -14, 112, -672, 3346, -14560, 57120, -206208, 694960, -2209774, 6683040, -19345760, 53874912, -144936288, 377965760, -958231680, 2367566866, -5713057728, 13488657168, -31210552800, 70873262880, -158145658560

Offset

0,2

Links

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

Formula

a(n) ~ (-1)^n * 49*exp(Pi*sqrt(7*n)) / (4096*n^(5/2)). - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^7, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^7. (End)

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^7, {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)^7) \\ Altug Alkan, Sep 20 2018

Crossrefs

Cf. A000122, A008451.

Sequence in context: A234800 A213348 A341368 * A002409 A155655 A007817

Adjacent sequences: A004405 A004406 A004407 * A004409 A004410 A004411

Keyword

sign

Author

N. J. A. Sloane

Status

approved