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%I #9 Sep 11 2022 10:06:42
%S 1,0,0,6,36,150,3780,77406,1059156,21669990,640319940,16622025486,
%T 450085011156,15416323450710,561938117029380,20587443165165246,
%U 835816881563118036,37282225483118856390,1722621978491064495300,83817942806509377794286
%N E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1)^3 * A(x).
%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. A349557, A357084.
%Y Cf. A357025.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 11 2022
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