A004406 Expansion of 1 / (Sum_{n=-oo..oo} x^(n^2))^5.

1, -10, 60, -280, 1110, -3912, 12600, -37760, 106620, -286290, 736184, -1822920, 4365800, -10149320, 22971120, -50744448, 109643350, -232145040, 482403060, -985229640, 1980034104, -3920000400, 7652388280, -14742829440

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

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

Crossrefs

Cf. A000122, A000132.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^5, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)

Formula

a(n) ~ (-1)^n * 5^(3/2)*exp(Pi*sqrt(5*n)) / (512*n^2). - Vaclav Kotesovec, Aug 18 2015

From Ilya Gutkovskiy, Sep 20 2018: (Start)

G.f.: 1/theta_3(x)^5, where theta_3() is the Jacobi theta function.

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^5. (End)