A341222 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^4.

1, 8, 36, 124, 362, 944, 2266, 5100, 10903, 22340, 44168, 84692, 158137, 288452, 515344, 903740, 1558465, 2646820, 4432964, 7329916, 11977507, 19358524, 30970444, 49077936, 77081679, 120054268, 185514428, 284540060, 433360308, 655622392, 985604644, 1472751228

Offset: 4

Author

Ilya Gutkovskiy, Feb 07 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..10000

Crossrefs

Column k=4 of A060642.

Cf. A000041, A023003, A048574, A327382, A341221, A341223, A341225, A341226, A341227, 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, 4):
seq(a(n), n=4..35);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 35; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^4, {x, 0, nmax}], x] // Drop[#, 4] &

Formula

a(n) ~ A023003(n). - Vaclav Kotesovec, Feb 20 2021