A004405 Expansion of 1 / (Sum_{n=-oo..oo} x^(n^2))^4.

1, -8, 40, -160, 552, -1712, 4896, -13120, 33320, -80872, 188784, -425952, 932640, -1988080, 4137024, -8422848, 16810536, -32943760, 63482760, -120440608, 225217904, -415498496, 756920160, -1362645440, 2425895712

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

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

Programs

Julia

# JacobiTheta3 is defined in A000122.
A004405List(len) = JacobiTheta3(len, -4)
A004405List(25) |> println # Peter Luschny, Mar 12 2018

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^4, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)

Formula

a(n) ~ (-1)^n * exp(2*Pi*sqrt(n)) / (32*n^(7/4)) * (1 - 35/(16*Pi*sqrt(n))). - Vaclav Kotesovec, Aug 18 2015, extended Jan 16 2017