A022696 Expansion of Product_{m>=1} (1 + m*q^m)^-4.

1, -4, 2, 0, 27, -36, 14, -104, 209, -392, 670, -728, 2278, -4444, 4808, -9800, 21750, -35604, 51906, -91120, 176285, -290444, 455168, -741336, 1372544, -2419348, 3490310, -5765744, 10788815, -17086420, 26221946, -44374160

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..3000

Crossrefs

Column k=4 of A297325.

Programs

Maple

N:= 100: # to get a(0)..a(N)
P:= mul((1+m*q^m)^(-4),m=1..N):
S:=series(P,q,N+1):
[seq(coeff(S,q,j),j=0..N)]; # Robert Israel, Jan 23 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-4, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 19 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^-4)) \\ G. C. Greubel, Jul 19 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