Triangle, read by rows, T(n, k) = (-1)^n*(n!/k!)^2*binomial(n-1, k-1).

Terms

a(0) =-1a(1) =4a(2) =1a(3) =-36a(4) =-18a(5) =-1a(6) =576a(7) =432a(8) =48a(9) =1a(10) =-14400a(11) =-14400a(12) =-2400a(13) =-100a(14) =-1a(15) =518400a(16) =648000a(17) =144000a(18) =9000a(19) =180a(20) =1a(21) =-25401600a(22) =-38102400a(23) =-10584000a(24) =-882000a(25) =-26460a(26) =-294a(27) =-1a(28) =1625702400a(29) =2844979200