A308444 a(0) = 1; a(n) = Sum_{k=1..n} Stirling2(n,k)*a(n-k).

1, 1, 2, 6, 27, 178, 1701, 23444, 464207, 13175526, 535353033, 31114680549, 2585577239479, 307143443783879, 52156058585285410, 12661558539485464967, 4394996515200407462730, 2181761307828685811029286, 1549298114199282873678255787, 1574165879361329032738370945407

Offset: 0

Author

Ilya Gutkovskiy, May 27 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..112

Crossrefs

Cf. A005121, A008277, A086555, A246040.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-j)*Stirling2(n, j), j=1..n))
    end:
seq(a(n), n=0..22);  # Alois P. Heinz, Feb 25 2025

Mathematica

a[n_] := a[n] = Sum[StirlingS2[n, k] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 19}]

Formula

log(a(n)) ~ n^2 * log(3) / 6. - Vaclav Kotesovec, May 28 2019