a(n) = Sum_{p|n, p prime} (-1)^(n/p+1) * (n-1)!/(p-1)!.

Terms

a(0) =0a(1) =1a(2) =1a(3) =-6a(4) =1a(5) =60a(6) =1a(7) =-5040a(8) =20160a(9) =347760a(10) =1a(11) =-59875200a(12) =1a(13) =6218372160a(14) =47221574400a(16) =1a(18) =1a(22) =1