A022733 Expansion of Product_{m>=1} 1/(1 - m*q^m)^9.

1, 9, 63, 354, 1764, 7947, 33294, 131049, 490437, 1756243, 6055749, 20190402, 65342031, 205853535, 632948256, 1903369146, 5608257129, 16216492509, 46080035361, 128829484620, 354757096107, 963099596421

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=9 of A297328.

Programs

Magma

n:=50; R:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^9:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-9, {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)^-9)) \\ G. C. Greubel, Jul 25 2018

Formula

G.f.: exp(9*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018