A022648 Expansion of Product_{m>=1} (1 + m*q^m)^20.

1, 20, 230, 2000, 14485, 91804, 524710, 2758520, 13526430, 62505180, 274345784, 1150868440, 4637343915, 18022311520, 67785066390, 247453832688, 878947211030, 3044142764520, 10299271911850, 34095293204360, 110599636109572, 351997976703180, 1100401056566170

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=20 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^20:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 17 2018

Maple

[seq(coeff(series(mul((1+m*q^m)^(20), m=1..100),q,101),q,j),j=0..25)]; # Muniru A Asiru, Feb 18 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^20, {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)^20)) \\ G. C. Greubel, Feb 17 2018