A341223 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^5.

1, 10, 55, 225, 765, 2287, 6215, 15680, 37265, 84300, 182933, 383070, 777705, 1536490, 2963120, 5592060, 10349465, 18817760, 33665870, 59341785, 103176877, 177131330, 300530125, 504318530, 837632700, 1377874861, 2246061540, 3630059510, 5819556060, 9258393655, 14622472250

Offset: 5

Author

Ilya Gutkovskiy, Feb 07 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..10000

Crossrefs

Column k=5 of A060642.

Cf. A000041, A023004, A048574, A327383, A341221, A341222, 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, 5):
seq(a(n), n=5..35);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 35; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &