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%I #13 Aug 17 2023 08:16:00
%S 1,1,5,46,641,11996,282907,8060242,269429729,10341367480,448317429011,
%T 21667926214694,1155321200076529,67370686916807236,
%U 4265392644606677963,291391173322695366106,21365209437807863776193,1673543873372595900318704
%N E.g.f. satisfies A(x) = exp(x * A(x) * (1 + x * A(x)^2)).
%F a(n) = n! * Sum_{k=0..n} (2*n-k+1)^(k-1) * binomial(k,n-k)/k!.
%o (PARI) a(n) = n!*sum(k=0, n, (2*n-k+1)^(k-1)*binomial(k, n-k)/k!);
%Y Cf. A088695, A362771, A363356.
%Y Cf. A365012.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 17 2023
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