%I #10 Oct 17 2023 08:19:18
%S 1,4,11,39,166,765,3716,18725,96956,512690,2756806,15027651,82853678,
%T 461215414,2588619402,14632777719,83232244238,476040155118,
%U 2736005962314,15793863291792,91530881427964,532343678619778,3106141476531628,18177446846299299
%N G.f. satisfies A(x) = (1 + x)^3 + x*A(x)^2.
%F G.f.: A(x) = 2*(1+x)^3 / (1+sqrt(1-4*x*(1+x)^3)).
%F a(n) = Sum_{k=0..n} binomial(3*(k+1),n-k) * binomial(2*k,k)/(k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(3*(k+1), n-k)*binomial(2*k, k)/(k+1));
%Y Cf. A025227, A366694.
%Y Cf. A162481.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 16 2023