A022632 Expansion of Product_{m>=1} (1 + m*q^m)^4.

1, 4, 14, 48, 137, 380, 998, 2488, 5996, 14020, 31868, 70616, 153389, 326248, 681914, 1402880, 2841769, 5678316, 11201956, 21833480, 42081245, 80264752, 151572328, 283577152, 525894397, 967100700, 1764378830, 3194682272, 5742739237, 10252117308, 18182247316

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 A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^4:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // Vincenzo Librandi, Jan 24 2018

Mathematica

CoefficientList[Take[Expand[Product[(1 + k x^k)^4, {k, 40}]], 40], x] (* Vincenzo Librandi, Jan 24 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^4)) \\ G. C. Greubel, Feb 16 2018

Formula

G.f.: exp(4*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018