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

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Column k=5 of A297323.

Sequence in context: A279700 A279603 A329252 * A114205 A316464 A167315

Adjacent sequences: A022662 A022663 A022664 * A022666 A022667 A022668

Keyword

sign

Author

N. J. A. Sloane

Extensions

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

Status

approved