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

Terms

a(0) =1a(1) =0a(2) =1a(3) =5a(4) =27a(5) =129a(6) =761a(7) =5137a(8) =40695a(9) =363815a(10) =3632629a(11) =39927183a(12) =479047667a(13) =6227155921a(14) =87178936305