A022634 Expansion of Product_{m>=1} (1 + m*q^m)^6.

1, 6, 27, 110, 387, 1266, 3896, 11340, 31629, 84992, 221028, 558450, 1375615, 3310764, 7803069, 18044374, 40998078, 91653990, 201842383, 438312534, 939439674, 1988944070, 4162521165, 8617025112, 17655688602, 35823617658, 72015578091, 143499705550, 283544586489, 555779906772

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 A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^6:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 17 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^6, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 17 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^6)) \\ G. C. Greubel, Feb 17 2018

Formula

G.f.: exp(6*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018