%I #8 Jul 28 2023 10:36:22

%S 1,1,1,2,7,22,62,182,583,1928,6358,21063,70888,241889,831634,2874584,

%T 9995579,34966279,122938956,434062141,1538378816,5471697241,

%U 19525345791,69880082323,250767909528,902123110483,3252793321513,11753570922933,42553831219830

%N G.f. satisfies A(x) = 1 + x*A(x) + x^3*A(x)^5.

%F a(n) = Sum_{k=0..floor(n/3)} binomial(n+2*k,5*k) * binomial(5*k,k) / (4*k+1).

%o (PARI) a(n) = sum(k=0, n\3, binomial(n+2*k, 5*k)*binomial(5*k, k)/(4*k+1));

%Y Cf. A063019, A182454, A349311, A364522.

%Y Cf. A023431, A071879, A215340.

%K nonn,easy

%O 0,4

%A _Seiichi Manyama_, Jul 28 2023