%I #15 Aug 19 2023 06:28:15

%S 1,1,7,55,709,11761,243181,6054763,175803097,5847578785,219175994521,

%T 9144024668131,420340277237365,21111584238219697,1150333949592549541,

%U 67589878866533749531,4260172601206280708401,286737199114729515029569

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

%H Michael De Vlieger, <a href="/A365030/b365030.txt">Table of n, a(n) for n = 0..363</a>

%F a(n) = n! * Sum_{k=0..n} (n-k+1)^(k-1) * binomial(3*k,n-k)/k!.

%t Array[#!*Sum[ (# - k + 1)^(k - 1)*Binomial[3 k, # - k]/k!, {k, 0, #}] &, 18, 0] (* _Michael De Vlieger_, Aug 18 2023 *)

%o (PARI) a(n) = n!*sum(k=0, n, (n-k+1)^(k-1)*binomial(3*k, n-k)/k!);

%Y Cf. A125500, A363744.

%Y Cf. A364938.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 17 2023