Triangle read by rows, T(n, k) = (-1)^k * RisingFactorial(n, k) * FallingFactorial(k - n, k).

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =2a(5) =0a(6) =1a(7) =6a(8) =24a(9) =0a(10) =1a(11) =12a(12) =120a(13) =720a(14) =0a(15) =1a(16) =20a(17) =360a(18) =5040a(19) =40320a(20) =0a(21) =1a(22) =30a(23) =840a(24) =20160a(25) =362880a(26) =3628800a(27) =0a(28) =1a(29) =42