%I #9 Sep 11 2022 10:06:59
%S 1,0,0,6,36,150,2340,47166,676116,10602150,248197860,6304530606,
%T 154511054676,4227889233750,134462460901860,4519745455581726,
%U 157756124072317716,5960350758700381830,243292987180534250340,10433760831781705395726,469420864688765414084436
%N E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3.
%F a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n-k+1)^(k-1) * Stirling2(n,3*k)/k!.
%o (PARI) a(n) = sum(k=0, n\3, (3*k)!*(n-k+1)^(k-1)*stirling(n, 3*k, 2)/k!);
%Y Cf. A349588, A357086.
%Y Cf. A357085, A357089.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 11 2022