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

0,2

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

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

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 *)

Prog

(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1+n*q^n)^3)) \\ G. C. Greubel, Feb 16 2018
(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

Crossrefs

Column k=3 of A297321.

Sequence in context: A032092 A026524 A282081 * A027346 A325218 A294958

Adjacent sequences: A022628 A022629 A022630 * A022632 A022633 A022634

Keyword

nonn

Author

N. J. A. Sloane

Status

approved