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%I #14 Aug 17 2023 08:16:12
%S 1,1,7,91,1809,48521,1643863,67381875,3243606817,179405231761,
%T 11213025902631,781604862035339,60120379931640625,5058593367221610009,
%U 462199816484860893559,45574025454771003821731,4823543138131670132557377,545448517762149418525390625
%N E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x)^2)).
%F a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(k,n-k)/k!.
%o (PARI) a(n) = n!*sum(k=0, n, (2*n+1)^(k-1)*binomial(k, n-k)/k!);
%Y Cf. A362773, A363357.
%Y Cf. A088695, A363479.
%Y Cf. A361093.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 17 2023
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