A004424 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-23).

1, -46, 1104, -18400, 239154, -2581152, 24056160, -198823040, 1485433104, -10177345486, 64663512288, -384402300960, 2153523131040, -11437761254432, 57880610587200, -280265903825280, 1303272560982834, -5838468742907712

Offset

0,2

Links

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

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 = 23 for this sequence. - Vaclav Kotesovec, Aug 18 2015

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1 / Pi^(23/4)) * Gamma(3/4)^23 = A388159. - Simon Plouffe, Sep 15 2025

Mathematica

nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^23, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)

Crossrefs

Sequence in context: A162452 A162186 A010998 * A361183 A258464 A320552

Adjacent sequences: A004421 A004422 A004423 * A004425 A004426 A004427

Keyword

sign

Author

N. J. A. Sloane

Status

approved