a(n) = n! - 2(n-1)! + 3(n-2)!.

Terms

a(0) =3a(1) =5a(2) =18a(3) =90a(4) =552a(5) =3960a(6) =32400a(7) =297360a(8) =3024000a(9) =33747840a(10) =410054400a(11) =5388768000a(12) =76161254400