A022728 Expansion of Product_{m>=1} (1-m*q^m)^-4.

1, 4, 18, 64, 219, 676, 2030, 5736, 15793, 41864, 108430, 273240, 675526, 1634780, 3891960, 9108872, 21018870, 47815572, 107446898, 238524144, 523812125, 1138233100, 2449710880, 5223395480, 11042278208

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) = 4, g(n) = n. - Seiichi Manyama, Dec 29 2017

Links

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

Crossrefs

Column k=4 of A297328.

Programs

Magma

n:=50; R:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^4:m in [1..n]])); // G. C. Greubel, Jul 25 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-4, {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)^-4)) \\ G. C. Greubel, Jul 25 2018

Formula

G.f.: exp(4*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018