A022635 Expansion of Product_{m>=1} (1 + m*q^m)^7.

1, 7, 35, 154, 588, 2065, 6790, 21071, 62447, 177863, 489279, 1305402, 3389603, 8587999, 21280436, 51674728, 123161500, 288539664, 665292642, 1511359766, 3386065697, 7488093282, 16357998447, 35324428405, 75453678433, 159512035137, 333918915120, 692516812176, 1423479123640

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=7 of A297321.

Programs

Magma

Coefficients(&*[(1+m*x^m)^7: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)^7, {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)^7)) \\ G. C. Greubel, Feb 17 2018

Formula

G.f.: exp(7*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018