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

0,2

Links

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

Formula

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

Prog

(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1-n*q^n)^-6)) \\ G. C. Greubel, Jul 25 2018
(Magma) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^6:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Crossrefs

Column k=6 of A297328.

Sequence in context: A074087 A297592 A255613 * A266944 A301272 A290921

Adjacent sequences: A022727 A022728 A022729 * A022731 A022732 A022733

Keyword

nonn

Author

N. J. A. Sloane

Status

approved