%I #7 Aug 15 2023 07:45:24

%S 1,1,8,117,2596,77705,2936406,134228059,7204913528,444331053873,

%T 30963240318250,2406301353714731,206354828717754036,

%U 19357367027097743449,1971809610601104110942,216754216326949771274715,25575749384428387961718256,3224227609551980271408565985

%N E.g.f. satisfies A(x) = 1 + x*A(x)^3*exp(x*A(x)).

%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(n+2*k+1,k)/( (n+2*k+1)*(n-k)! ).

%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(n+2*k+1, k)/((n+2*k+1)*(n-k)!));

%Y Cf. A364983, A364985, A364986.

%Y Cf. A108447.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 15 2023