%I #14 Mar 31 2024 08:47:16
%S 1,2,9,54,372,2778,21873,178786,1502649,12904524,112741664,998871030,
%T 8953443276,81047485148,739846170864,6803054508702,62954736555836,
%U 585850907166084,5479077065774682,51470699845616004,485456696541512442,4595280949098247422
%N G.f. satisfies A(x) = 1 + x * A(x)^(3/2) * (1 + A(x)^(3/2)).
%F a(n) = Sum{k=0..n} binomial(n,k) * binomial(3*n/2+3*k/2+1,n)/(3*n/2+3*k/2+1).
%o (PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(3*n/2+3*k/2+1, n)/(3*n/2+3*k/2+1));
%Y Cf. A006013, A370475.
%Y Cf. A262441, A366400.
%Y Cf. A271469.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 31 2024