A022636 Expansion of Product_{m>=1} (1 + m*q^m)^8.

1, 8, 44, 208, 854, 3200, 11176, 36752, 115089, 345600, 1000484, 2804544, 7639718, 20280672, 52593032, 133509840, 332340788, 812455304, 1953140484, 4622589504, 10782030284, 24807035200, 56345836888, 126438750160, 280490520517, 615512622608, 1336825948592, 2875079590304

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Column k=8 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^8:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 17 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^8, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 17 2018 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^8)) \\ G. C. Greubel, Feb 17 2018

Formula

G.f.: exp(8*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018