A022668 Expansion of Product_{m>=1} (1 - m*q^m)^8.

1, -8, 12, 48, -106, -128, 8, 880, 1041, -2560, -2524, -6720, 5030, 30880, 26696, 9264, -136524, -152456, -172604, 37824, 938316, 1568960, 1225624, -1981904, -4585531, -10791440, -8363184, 2558560, 29452194, 67002976, 59590976, 77029104, -140261287, -367505912, -536229932

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=8 of A297323.

Programs

Magma

Coefficients(&*[(1-m*x^m)^8: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)^8, {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)^8)) \\ G. C. Greubel, Feb 24 2018

Formula

G.f.: exp(-8*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Extensions

Terms a(30) onward added by G. C. Greubel, Feb 24 2018