a(n) = Sum_{k=0..n} binomial(4*k,n-k) * Catalan(k).

Terms

a(0) =1a(1) =1a(2) =6a(3) =27a(4) =134a(5) =709a(6) =3892a(7) =22004a(8) =127250a(9) =749230a(10) =4476386a(11) =27071344a(12) =165398868a(13) =1019405720a(14) =6330482488a(15) =39571612357a(16) =248796862550