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%I #8 Aug 14 2023 08:28:01
%S 1,1,9,124,2525,68616,2338357,96004672,4616135001,254542038400,
%T 15839013320801,1098078537291264,83940831427695541,
%U 7014958697801657344,636298582947212386125,62261039244978489081856,6537251350698278868150833,733159568772947522820538368
%N E.g.f. satisfies A(x) = exp( x*A(x) / (1 - x*A(x))^3 ).
%F a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(n+2*k-1,n-k)/k!.
%o (PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(n+2*k-1, n-k)/k!);
%Y Cf. A052873, A364939.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 14 2023
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