A022669 Expansion of Product_{m>=1} (1 - m*q^m)^9.

1, -9, 18, 51, -171, -117, 249, 1251, 531, -5599, -3006, -2295, 20664, 50508, -6354, -78597, -292887, -105273, 268957, 792414, 1974312, 825753, -2605185, -9778671, -9956433, -4944978, 19214991, 57418523, 78518664, 60044976, -124946361, -247193622, -634049649, -623771424, 218263050

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=9 of A297323.

Programs

Magma

Coefficients(&*[(1-m*x^m)^9: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)^9, {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)^9)) \\ G. C. Greubel, Feb 24 2018

Formula

G.f.: exp(-9*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Extensions

Terms a(29) onward added by G. C. Greubel, Feb 24 2018