a(n) = Sum_{k=0..n} binomial(2*n,n+k)*3^k.

Terms

a(0) =1a(1) =5a(2) =27a(3) =146a(4) =787a(5) =4230a(6) =22686a(7) =121476a(8) =649731a(9) =3472382a(10) =18546922a(11) =99023292a(12) =528535726a(13) =2820451964a(14) =15048601308a(15) =80283276936a(16) =428271193827