A022730 Expansion of Product_{m>=1} 1/(1 - m*q^m)^6.

1, 6, 33, 146, 594, 2196, 7687, 25410, 80664, 246258, 728610, 2093334, 5865853, 16057998, 43063812, 113293158, 292928448, 745216692, 1867840830, 4616732712, 11264133069, 27149243724, 64691795178

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=6 of A297328.

Programs

Magma

n:=50; R:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^6:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-6, {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)^-6)) \\ G. C. Greubel, Jul 25 2018

Formula

G.f.: exp(6*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018