%I #10 Aug 25 2023 09:43:18
%S 1,1,5,33,252,2091,18319,166750,1561599,14948572,145615404,1438752770,
%T 14384289530,145248707646,1479212551278,15175516654760,
%U 156691764630780,1627069871618145,16980373299730925,178006989972532900,1873607777794186000
%N G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)^3).
%F a(n) = Sum_{k=0..n} binomial(3*n+k+1,k) * binomial(k,n-k)/(3*n+k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(3*n+k+1, k)*binomial(k, n-k)/(3*n+k+1));
%Y Cf. A002294, A365178, A365180, A365181, A365183.
%Y Cf. A365177.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 25 2023