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G.f. A(x) satisfies A(x) = 1/( 1 - x * (1 + 9*x)^(1/3) * A(x)^2 ).
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%I #8 Apr 20 2024 10:27:50

%S 1,1,6,21,181,771,7728,34689,385632,1732971,21041598,92147697,

%T 1217109951,5099210686,73380609681,289623783084,4564472639880,

%U 16722146775195,290985244619874,974044248064611,18925364858562927,56848541164586820,1251693011560795635

%N G.f. A(x) satisfies A(x) = 1/( 1 - x * (1 + 9*x)^(1/3) * A(x)^2 ).

%F a(n) = Sum_{k=0..n} 9^(n-k) * binomial(3*k,k) * binomial(k/3,n-k)/(2*k+1).

%o (PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(3*k, k)*binomial(k/3, n-k)/(2*k+1));

%Y Cf. A364475, A372139.

%Y Cf. A372124.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 20 2024