%I #8 Jul 19 2023 07:48:27

%S 1,2,17,204,2852,43489,701438,11767095,203223146,3589167533,

%T 64524575635,1176860764416,21723084076739,405038036077647,

%U 7617437252889030,144328483391622298,2752414654270742784,52790626691557217602,1017655117382823639414,19706520281177438174530

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

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

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

%Y Cf. A215624, A234525, A239108, A364331, A364338.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 18 2023