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

Terms

a(0) =1a(1) =4a(2) =14a(3) =80a(4) =345a(5) =1336a(6) =5074a(7) =18404a(8) =64460a(9) =220276a(10) =736242a(11) =2415128a(12) =7798043a(13) =24833160a(14) =78131242a(15) =243211412a(16) =749926963a(17) =2292771088a(18) =6956262660a(19) =20959406680a(20) =62753991192a(21) =186809711448a(22) =553172044548