A022613 Expansion of Product_{m>=1} (1+q^m)^(-18).

1, -18, 153, -834, 3384, -11340, 33729, -92430, 236727, -572120, 1318743, -2922948, 6259641, -13000770, 26283159, -51879720, 100210041, -189775800, 352975681, -645780060, 1163610432, -2067225594, 3624593265, -6277838652

Offset

0,2

Links

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

Formula

a(n) ~ (-1)^n * 3^(1/4) * exp(Pi*sqrt(3*n)) / (2^(3/2) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

a(0) = 1, a(n) = -(18/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 05 2017

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = 4 * exp(-3*Pi/4) * 2^(1/4) = A388337. - Simon Plouffe, Sep 15 2025

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^18, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Crossrefs

Sequence in context: A252971 A047643 A010934 * A060221 A244876 A171741

Adjacent sequences: A022610 A022611 A022612 * A022614 A022615 A022616

Keyword

sign

Author

N. J. A. Sloane

Status

approved