a(n) = (n+3)*n!/2.

Terms

a(0) =2a(1) =5a(2) =18a(3) =84a(4) =480a(5) =3240a(6) =25200a(7) =221760a(8) =2177280a(9) =23587200a(10) =279417600a(11) =3592512000a(12) =49816166400a(13) =741015475200