A022665 Expansion of Product_{m>=1} (1 - m*q^m)^5.

1, -5, 0, 25, 0, -26, -145, 0, 265, 265, 993, -825, -2070, -3190, -2335, 2739, 7890, 29570, 21085, -5250, -73006, -71945, -191140, -176805, 185045, 295675, 1204590, 1067375, 1353655, -910885, -3688009, -4645850, -9409195, -12021485, -4296815, 19981183, 28942560, 76843230, 70996895

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=5 of A297323.

Programs

Magma

Coefficients(&*[(1-m*x^m)^5:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 23 2018

Mathematica

With[{nmax=50}, CoefficientList[Series[Product[(1-k*q^k)^5, {k,1,nmax}], {q, 0, nmax}],q]] (* G. C. Greubel, Feb 23 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^5)) \\ G. C. Greubel, Feb 23 2018

Formula

G.f.: exp(-5*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Extensions

Terms a(32) onward added by G. C. Greubel, Feb 23 2018