A022637 Expansion of Product_{m>=1} (1 + m*q^m)^9.

1, 9, 54, 273, 1197, 4761, 17577, 60957, 200799, 633007, 1920510, 5633667, 16037700, 44439840, 120165858, 317762553, 823240341, 2092864401, 5228118701, 12848849154, 31100190048, 74208885351, 174708121455, 406132690635, 932871440739, 2118595079790, 4759875472491

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=9 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^9: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)^9, {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)^9)) \\ G. C. Greubel, Feb 17 2018

Formula

G.f.: exp(9*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018