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G.f. satisfies A(x) = 1 + x * A(x)^(3/2) * (1 + A(x)^(3/2)).
2

%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