%I #13 Jan 29 2024 09:46:57

%S 1,3,6,11,24,66,196,576,1692,5110,15933,50604,161988,521700,1693362,

%T 5541679,18260055,60487659,201272437,672550158,2256204327,7596059333,

%U 25655943417,86904524289,295154911774,1004906765178,3429178160346,11726499288028,40178538608682

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

%F a(n) = Sum_{k=0..floor(n/3)} binomial(n+3*k+2,n-3*k) * binomial(3*k,k) / (2*k+1).

%o (PARI) a(n) = sum(k=0, n\3, binomial(n+3*k+2, n-3*k)*binomial(3*k, k)/(2*k+1));

%Y Cf. A364623, A364626.

%Y Cf. A086615, A369693.

%Y Cf. A364589.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 29 2024