A022727 Expansion of Product_{m>=1} (1-m*q^m)^-3.

1, 3, 12, 37, 114, 312, 855, 2178, 5496, 13302, 31719, 73482, 168086, 375984, 830976, 1805887, 3880746, 8225460, 17262440, 35809446, 73621776, 149875003, 302635110, 605861124, 1204043358, 2374645746

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 A297328.

Programs

Magma

n:=50; R:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^3:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-3, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 25 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-3)) \\ G. C. Greubel, Jul 25 2018

Formula

G.f.: exp(3*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018