%I #11 Aug 18 2023 08:26:43
%S 1,1,11,175,4317,142561,5929513,297901899,17557448681,1188110627137,
%T 90804918357261,7737033497254579,727253150819898541,
%U 74760871323339663489,8344094871249960257009,1004872166403751985971291,129883465213311163328142417
%N E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))^3).
%F a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(3*k,n-k)/k!.
%o (PARI) a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(3*k, n-k)/k!);
%Y Cf. A363357, A365033.
%Y Cf. A364942.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 17 2023