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

%I A308444 #11 Feb 26 2025 09:28:02
%S A308444 1,1,2,6,27,178,1701,23444,464207,13175526,535353033,31114680549,
%T A308444 2585577239479,307143443783879,52156058585285410,12661558539485464967,
%U A308444 4394996515200407462730,2181761307828685811029286,1549298114199282873678255787,1574165879361329032738370945407
%N A308444 a(0) = 1; a(n) = Sum_{k=1..n} Stirling2(n,k)*a(n-k).
%H A308444 Alois P. Heinz, <a href="/A308444/b308444.txt">Table of n, a(n) for n = 0..112</a>
%F A308444 log(a(n)) ~ n^2 * log(3) / 6. - _Vaclav Kotesovec_, May 28 2019
%p A308444 a:= proc(n) option remember; `if`(n=0, 1,
%p A308444       add(a(n-j)*Stirling2(n, j), j=1..n))
%p A308444     end:
%p A308444 seq(a(n), n=0..22);  # _Alois P. Heinz_, Feb 25 2025
%t A308444 a[n_] := a[n] = Sum[StirlingS2[n, k] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 19}]
%Y A308444 Cf. A005121, A008277, A086555, A246040.
%K A308444 nonn
%O A308444 0,3
%A A308444 _Ilya Gutkovskiy_, May 27 2019