A306173 a(n) is the n-th term of the inverse Euler transform of j-> n^(j-1).

1, 1, 6, 42, 420, 5155, 77658, 1376340, 28133616, 651317463, 16846515510, 481472570920, 15067838554860, 512473599799551, 18821719654854998, 742395982266536520, 31299550394528466960, 1404629090174946183156, 66851805805525048040334, 3363381327122496643643628

Offset: 1

Author

Alois P. Heinz, Jun 23 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..200

Crossrefs

Main diagonal of A065177.

Cf. A075147, A316073.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(g(i, k)+j-1, j)*b(n-i*j, i-1,k), j=0..n/i)))
    end:
g:= proc(n, k) option remember; k^(n-1)-b(n, n-1, k) end:
a:= n-> g(n$2):
seq(a(n), n=1..21);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[g[i, k] + j - 1, j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]];
g[n_, k_] := g[n, k] = k^(n - 1) - b[n, n - 1, k];
a[n_] := g[n, n];
a /@ Range[21] (* Jean-François Alcover, Jan 06 2020, after Alois P. Heinz *)

Formula

a(n) ~ (1 - exp(-1)) * n^(n-1). - Vaclav Kotesovec, Oct 08 2019