A022617 Expansion of Product_{m>=1} (1+q^m)^(-22).

1, -22, 231, -1562, 7799, -31438, 109208, -341660, 987327, -2672868, 6848490, -16752958, 39388481, -89439944, 196910681, -421739450, 881199561, -1800336692, 3603535166, -7078509064, 13665905671

Offset

0,2

Links

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

Formula

a(n) ~ (-1)^n * 11^(1/4) * exp(Pi*sqrt(11*n/3)) / (2^(3/2) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

a(0) = 1, a(n) = -(22/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(-11*Pi/12) * 2^(3/4) = A388341. - Simon Plouffe, Sep 15 2025

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 + x^k)^22, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Crossrefs

Sequence in context: A003909 A047647 A010938 * A082205 A003205 A037268

Adjacent sequences: A022614 A022615 A022616 * A022618 A022619 A022620

Keyword

sign

Author

N. J. A. Sloane

Status

approved