A022666 Expansion of Product_{m>=1} (1 - m*q^m)^6.

1, -6, 3, 34, -21, -66, -168, 180, 645, 176, 540, -3282, -4265, -1068, 5805, 21226, 16398, 27498, -42993, -139110, -199998, -46374, 127917, 467016, 1424954, 881958, 895899, -2559102, -5166543, -9792708, -11899179, 5560560, 13493076, 39293062, 65560674, 94059054, 14988615

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 A297323.

Programs

Magma

Coefficients(&*[(1-m*x^m)^6:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 24 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^6, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 24 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^6)) \\ G. C. Greubel, Feb 24 2018

Formula

G.f.: exp(-6*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Extensions

Terms a(31) onward added by G. C. Greubel, Feb 24 2018