%I #11 Mar 26 2024 11:15:11
%S 1,3,24,235,2586,30603,380359,4896753,64731747,873539236,11984536632,
%T 166661420814,2343950447112,33282048811530,476462982915993,
%U 6869620848003570,99663539644072305,1453861111238442363,21312207036239313936,313783619269186619589
%N G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^3.
%F a(n) = 3 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+2,k)/(5*k+3).
%F G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A349333.
%o (PARI) a(n) = 3*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+2, k)/(5*k+3));
%Y Cf. A349333, A371379, A371519, A371521, A371523.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 26 2024