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%I #8 Sep 11 2022 10:07:18
%S 1,0,0,1,6,25,140,1561,19586,228425,2870160,44172601,780614846,
%T 14499946825,284310704860,6089231941521,142225796401786,
%U 3537029819020905,92766573133851240,2577870903366020521,75999605064376599606,2362944241092314079145
%N E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3 / 6.
%F a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n-k+1)^(k-1) * Stirling2(n,3*k)/(6^k * k!).
%o (PARI) a(n) = sum(k=0, n\3, (3*k)!*(n-k+1)^(k-1)*stirling(n, 3*k, 2)/(6^k*k!));
%Y Cf. A349588, A357088.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Sep 11 2022
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