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A004405 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-4). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

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 *)

PROG

(Julia) # JacobiTheta3 is defined in A000122.

A004405List(len) = JacobiTheta3(len, -4)

A004405List(25) |> println # Peter Luschny, Mar 12 2018

CROSSREFS

Sequence in context: A264602 A125198 A128639 * A284286 A001789 A074412

Adjacent sequences:  A004402 A004403 A004404 * A004406 A004407 A004408

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 25 12:00 EDT 2019. Contains 324352 sequences. (Running on oeis4.)