Triangle, read by rows, T(n, k) = (-1)^n * n!/(k*k!) * binomial(n-1, k-1) * binomial(n, k-1).

Terms

a(0) =-1a(1) =2a(2) =1a(3) =-6a(4) =-9a(5) =-1a(6) =24a(7) =72a(8) =24a(9) =1a(10) =-120a(11) =-600a(12) =-400a(13) =-50a(14) =-1a(15) =720a(16) =5400a(17) =6000a(18) =1500a(19) =90a(20) =1a(21) =-5040a(22) =-52920a(23) =-88200a(24) =-36750a(25) =-4410a(26) =-147a(27) =-1a(28) =40320a(29) =564480