%I #9 Apr 03 2024 11:12:40
%S 1,6,66,926,14706,251622,4524786,84310014,1613384994,31521329670,
%T 626151135330,12608193099294,256769542135314,5279533270393446,
%U 109449833201392530,2285215031994672894,48011502768234360642,1014265693597636966662
%N G.f. satisfies A(x) = ( 1 + x * A(x) * (1 + A(x)) )^3.
%F G.f.: B(x)^3 where B(x) is the g.f. of A364167.
%F a(n) = Sum_{k=0..n} binomial(n,k) * binomial(3*n+3*k+3,n)/(n+k+1).
%o (PARI) a(n, r=3, t=3, u=3) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));
%Y Cf. A006318, A371693.
%Y Cf. A364167.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 02 2024