A022698 Expansion of Product_{m>=1} 1/(1 + m*q^m)^6.

1, -6, 9, -2, 42, -132, 95, -210, 840, -1394, 2442, -4374, 8589, -20862, 31812, -48758, 119856, -222228, 347038, -631992, 1220781, -2228812, 3730962, -6390948, 11861066, -21539358, 35874624, -59882714, 110055054

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=6 of A297325.

Programs

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-6, {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)^-6)) \\ G. C. Greubel, Jul 19 2018

Formula

G.f.: exp(-6*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018