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%I #10 Nov 05 2023 09:01:34
%S 1,1,0,2,6,6,14,60,120,216,732,2028,4240,11280,33696,83328,207072,
%T 591360,1606752,4102656,11172528,31167280,83112000,223249824,
%U 619860960,1699634784,4603619616,12689107200,35170240512,96523315200,265883115264,738668408064
%N G.f. satisfies A(x) = 1 + x + 2*x^3*A(x)^3.
%F a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*k+1,n-3*k) * A001764(k).
%o (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*k+1, n-3*k)*binomial(3*k, k)/(2*k+1));
%Y Cf. A001764, A366555, A367073, A367074.
%Y Cf. A367111.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Nov 05 2023