Triangular array read by rows: [T(n,k),k=1..tau(n)] = [-n!/(d*(-(n/d)!)^d), d|n].

Terms

a(0) =1a(1) =1a(2) =-1a(3) =1a(4) =2a(5) =1a(6) =-3a(7) =-6a(8) =1a(9) =24a(10) =1a(11) =-10a(12) =30a(13) =-120a(14) =1a(15) =720a(16) =1a(17) =-35a(18) =-630a(19) =-5040a(20) =1a(21) =560a(22) =40320a(23) =1a(24) =-126a(25) =22680a(26) =-362880a(27) =1a(28) =3628800a(29) =1