a(n) = (2n+4)!/(4!*n!*(n+1)!).

Terms

a(0) =1a(1) =15a(2) =140a(3) =1050a(4) =6930a(5) =42042a(6) =240240a(7) =1312740a(8) =6928350a(9) =35565530a(10) =178474296a(11) =878850700a(12) =4259045700a(13) =20359174500a(14) =96172862400a(15) =449608131720