%I #8 Aug 23 2023 08:36:14
%S 1,3,18,130,1041,8889,79310,730593,6895575,66337179,648087750,
%T 6412437474,64125877361,647102364990,6581050832082,67384499298690,
%U 694077333315363,7186898222178342,74767377019254450,781105293655408554,8191332027277068543
%N G.f. satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^2)^3.
%F If g.f. satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^s)^t, then a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(t*(n+1),k) * binomial(n+(s-1)*k-1,n-k).
%o (PARI) a(n, s=2, t=3) = sum(k=0, n, binomial(t*(n+1), k)*binomial(n+(s-1)*k-1, n-k))/(n+1);
%Y Cf. A109081, A365133.
%Y Cf. A365121.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Aug 23 2023