%I #12 Aug 28 2022 04:24:32
%S 1,0,2,3,88,485,13896,158767,4919664,90698841,3130084360,81025744811,
%T 3144372342552,104942286748741,4582896912897408,186591555463556895,
%U 9135453970592830816,437146665470130792497,23852990622867670807704,1307029600226135900982835
%N E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x)^2.
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n+k+1)^(k-1) * Stirling2(n-k,k)/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, (n+k+1)^(k-1)*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A349560, A356785, A356789.
%Y Cf. A355762.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 27 2022