%I #8 Jul 26 2023 18:02:47

%S 1,1,3,13,65,353,2024,12057,73890,462851,2950261,19073921,124776881,

%T 824409052,5493384031,36874564529,249114808794,1692489908494,

%U 11556616157589,79265016880139,545860966841247,3772800724433931,26162662010039826,181974370638420829

%N G.f. satisfies A(x) = 1 + x*A(x)^2 + x^2*A(x)^6.

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

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

%Y Cf. A001002, A001764, A006605, A052709, A143330, A364477.

%Y Cf. A364472, A364474.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 26 2023