A341227 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^8.

1, 16, 136, 824, 4004, 16608, 61076, 204200, 631714, 1831752, 5027312, 13159104, 33049090, 80030808, 187613348, 427201176, 947520103, 2051989360, 4347996772, 9030416704, 18412343832, 36905322248, 72807201940, 141525042736, 271321432489, 513454659312

Offset: 8

Author

Ilya Gutkovskiy, Feb 07 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..10000

Crossrefs

Column k=8 of A060642.

Cf. A000041, A023007, A048574, A327386, A341221, A341222, A341223, A341225, A341226, A341228.

Programs

Maple

b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, combinat[
      numbpart](n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..33);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 33; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &