a(n) = n! * Sum_{d|n} n^d / d!.

Terms

a(0) =1a(1) =8a(2) =45a(3) =544a(4) =3725a(5) =89856a(6) =858823a(7) =25271296a(8) =434776329a(9) =13241728000a(10) =285750755411