Triangle read by rows: T(n, k) = (-1)^k*(k+1)*(n+1-k)!, n >= 0, k = 0..n.

Terms

a(0) =1a(1) =2a(2) =-2a(3) =6a(4) =-4a(5) =3a(6) =24a(7) =-12a(8) =6a(9) =-4a(10) =120a(11) =-48a(12) =18a(13) =-8a(14) =5a(15) =720a(16) =-240a(17) =72a(18) =-24a(19) =10a(20) =-6a(21) =5040a(22) =-1440a(23) =360a(24) =-96a(25) =30a(26) =-12a(27) =7a(28) =40320a(29) =-10080