A293554 a(n) = [x^n] exp(Sum_{k>=1} x^k/(k*(1 - x^k)^n)).

1, 1, 3, 10, 45, 216, 1232, 7624, 52215, 385495, 3056680, 25825669, 231503636, 2191866327, 21835650219, 228089127908, 2490775088645, 28362322146780, 336015253520857, 4133561828779865, 52705520063966840, 695406327616587268, 9480212057583970983

Offset: 0

Author

Ilya Gutkovskiy, Oct 11 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..537
• N. J. A. Sloane, Transforms

Crossrefs

Main diagonal of A293551.

Programs

Maple

with(numtheory):
b:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*
      binomial(d+k-2, k-1), d=divisors(j))*b(n-j, k), j=1..n)/n)
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 17 2017

Mathematica

Table[SeriesCoefficient[E^(Sum[x^k/(k (1 - x^k)^n), {k, 1, n}]), {x, 0, n}], {n, 0, 22}]
Table[SeriesCoefficient[Product[1/(1 - x^k)^Binomial[n + k - 2, n - 1], {k, 1, n}], {x, 0, n}], {n, 0, 22}]

Formula

a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^binomial(n+k-2,n-1).

a(n) = A293551(n,n).