A004416 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-15).

1, -30, 480, -5440, 48930, -371136, 2464320, -14688000, 80001120, -403533790, 1904433984, -8477603520, 35829727680, -144548556480, 559157308800, -2081866609920, 7484792950050, -26057409056640, 88057506412320

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

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

Crossrefs

Cf. A000122, A276287.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^15, {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)^15) \\ Altug Alkan, Sep 20 2018

Formula

a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 15 for this sequence. - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^15, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^15. (End)