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

Terms

a(0) =-3a(1) =-1a(2) =6a(3) =54a(4) =408a(5) =3240a(6) =28080a(7) =267120a(8) =2782080a(9) =31570560a(10) =388281600a(11) =5149267200a(12) =73287244800