%I #13 Aug 17 2023 08:16:08
%S 1,1,7,85,1581,39501,1244953,47426373,2120506489,108894505753,
%T 6317267871501,408637512353049,29164082035045477,2276557391070945477,
%U 192956160476285907457,17647873882378895267821,1732445579330211460781937,181694902682241512454842673
%N E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))).
%F a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(k,n-k)/k!.
%o (PARI) a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(k, n-k)/k!);
%Y Cf. A362773, A363358.
%Y Cf. A361142.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 17 2023