A022732 Expansion of Product_{m>=1} 1/(1 - m*q^m)^8.

1, 8, 52, 272, 1274, 5408, 21448, 80080, 285043, 972496, 3200644, 10199456, 31592350, 95366176, 281269560, 812094448, 2299480441, 6394796832, 17489643664, 47096042032, 124993380566, 327249781952

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=8 of A297328.

Programs

Magma

n:=50; R:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^8:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-8, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 25 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-8)) \\ G. C. Greubel, Jul 25 2018

Formula

G.f.: exp(8*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018