A022643 Expansion of Product_{m>=1} (1 + m*q^m)^15.

1, 15, 135, 950, 5670, 30003, 144680, 647055, 2717760, 10820640, 41128374, 150073470, 528074655, 1798537380, 5947216050, 19142919543, 60113026305, 184513760775, 554517086825, 1634047143090, 4727605374594, 13444544485435, 37620762642885, 103678546403985, 281639925782930

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=15 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^15: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)^(15), 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)^15, {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)^15)) \\ G. C. Greubel, Feb 17 2018