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G.f. satisfies A(x) = ( 1 + x * A(x) * (1 + A(x)) )^3.
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%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