A022631 Expansion of Product_{m>=1} (1 + m*q^m)^3.

1, 3, 9, 28, 69, 174, 413, 933, 2046, 4391, 9168, 18675, 37522, 73725, 142893, 273159, 514512, 957666, 1762837, 3208884, 5783727, 10330732, 18280590, 32086827, 55880614, 96579240, 165733335, 282513246, 478419366, 805196022, 1347288750, 2241377166, 3708721887

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -3, g(n) = -n. - Seiichi Manyama, Dec 29 2017

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=3 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^3:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 16 2018

Mathematica

With[{nmax=34}, CoefficientList[Series[Product[(1+k*q^k)^3, {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)^3)) \\ G. C. Greubel, Feb 16 2018

Formula

G.f.: exp(3*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018