%I #14 Apr 02 2024 08:53:46

%S 1,3,36,603,11745,249372,5599044,130735620,3142426428,77238209502,

%T 1932396279066,49047725266101,1259884849971465,32690034127387431,

%U 855528520866461010,22556952666651901761,598607836414445357145,15976563963437863357146

%N G.f. satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x) + A(x)^2).

%H Seiichi Manyama, <a href="/A371660/b371660.txt">Table of n, a(n) for n = 0..685</a>

%F a(n) = (1/n) * Sum_{k=0..floor(n-1)/2} 3^(n-k) * binomial(n,k) * binomial(4*n-k,n-1-2*k) for n > 0.

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

%Y Cf. A271469, A363311, A371661.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 01 2024