a(n) = binomial(2n+1, n+1)*binomial(n+3, 3).

Terms

a(0) =1a(1) =12a(2) =100a(3) =700a(4) =4410a(5) =25872a(6) =144144a(7) =772200a(8) =4011150a(9) =20323160a(10) =100876776a(11) =492156392a(12) =2366136500a(13) =11232648000a(14) =52739956800a(15) =245240799120