A022633 Expansion of Product_{m>=1} (1 + m*q^m)^5.

1, 5, 20, 75, 240, 726, 2075, 5620, 14645, 36875, 90057, 214065, 497170, 1129670, 2517425, 5512125, 11871310, 25184930, 52686885, 108786970, 221894842, 447455885, 892609420, 1762608545, 3447282925, 6680871925, 12835968690, 24459374345, 46243132855, 86773966825, 161664667295

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=5 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^5:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 16 2018

Mathematica

With[{nmax=50}, CoefficientList[Series[Product[(1+k*q^k)^5, {k,1,nmax}], {q, 0, nmax}],q]] (* G. C. Greubel, Feb 16 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^5)) \\ G. C. Greubel, Feb 16 2018

Formula

G.f.: exp(5*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018