%I #10 Oct 14 2023 14:00:00
%S 1,1,0,0,1,3,3,1,3,15,30,30,27,87,252,420,475,747,2064,4632,7203,9933,
%T 19635,47025,92013,144745,237510,498498,1073817,1969131,3267411,
%U 5977881,12462579,25035747,45090936,79414344,153115299,311198457,600883569,1090988379,2012793705
%N G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^3.
%F a(n) = Sum_{k=0..floor(n/4)} binomial(2*k+1,n-4*k) * binomial(3*k,k)/(2*k+1).
%F a(n) = A366592(n) + A366592(n-1).
%o (PARI) a(n) = sum(k=0, n\4, binomial(2*k+1, n-4*k)*binomial(3*k, k)/(2*k+1));
%Y Cf. A019497, A366266, A366555.
%Y Cf. A366554, A366558.
%Y Cf. A366592.
%K nonn
%O 0,6
%A _Seiichi Manyama_, Oct 13 2023