%I #10 Sep 10 2022 08:51:06
%S 1,0,0,6,36,150,3060,62286,867636,15591750,419764500,10834588446,
%T 277719263316,8580282719190,297021183388020,10459810717672686,
%U 393932179466738676,16351788886638987750,717798906181149294420,32905220431196072057406
%N E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^3.
%F a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+1)^(k-1) * Stirling2(n,3*k)/k!.
%o (PARI) a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*stirling(n, 3*k, 2)/k!);
%Y Cf. A030019, A357024.
%Y Cf. A353664, A357010, A357032.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 09 2022