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%I #10 Nov 10 2023 04:29:56
%S 1,1,7,92,1824,48804,1649724,67492872,3243567552,179139978072,
%T 11181615816216,778466939121552,59811143359463952,5027200928936108064,
%U 458865351655379262432,45201262487568977507328,4779609140451030860102400,539990133396500652971120640
%N E.g.f. satisfies A(x) = 1 - A(x)^3 * log(1 - x).
%F a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * |Stirling1(n,k)|.
%F a(n) ~ 9 * n^(n-1) / (2^(5/2) * exp(23*n/27) * (exp(4/27) - 1)^(n - 1/2)). - _Vaclav Kotesovec_, Nov 10 2023
%t Table[Sum[(-1)^(n-k) * (3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 10 2023 *)
%o (PARI) a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*abs(stirling(n, k, 1)));
%Y Cf. A367155, A367161, A367164.
%Y Cf. A052803.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 07 2023