a(n) = Sum_{r < n, gcd(r,n)=1} n!/r.

Terms

a(0) =1a(1) =2a(2) =9a(3) =32a(4) =250a(5) =864a(6) =12348a(7) =67584a(8) =804816a(9) =5760000a(10) =116915040a(11) =686776320a(12) =19323757440a(13) =157991178240