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%I #8 Aug 25 2023 09:43:11
%S 1,1,10,195,5836,236925,12177966,758458603,55528414264,4674208189977,
%T 444823048027450,47227542351423951,5534636939373353604,
%U 709653811287800826421,98825110036657191358822,14853654178825132742729715,2396666529204491489278153456
%N E.g.f. satisfies A(x) = 1 + x*A(x)^4*exp(x*A(x)^2).
%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(2*n+2*k+1,k)/( (2*n+2*k+1)*(n-k)! ).
%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(2*n+2*k+1, k)/((2*n+2*k+1)*(n-k)!));
%Y Cf. A364987, A364989, A365175, A365177.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 25 2023
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