%I #19 Mar 13 2024 13:17:30
%S 1,0,2,3,112,665,23016,292957,10710960,223877313,9010822600,
%T 266949248621,12012620436312,461111201730049,23286625765980864,
%U 1093225826724243045,61822510319788946656,3415325919719802626177,215162865022831595415576
%N E.g.f. satisfies log(A(x)) = x*A(x)^2 * (exp(x*A(x)^2) - 1).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (2*n+1)^(k-1) * Stirling2(n-k,k)/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, (2*n+1)^(k-1)*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A356785, A356788, A356797.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 12 2024