Triangle T(n,k)= n! if k=0, T(n,k) = -(n-k)!*A003319(k) if k > 0.

Terms

a(0) =1a(1) =1a(2) =-1a(3) =2a(4) =-1a(5) =-1a(6) =6a(7) =-2a(8) =-1a(9) =-3a(10) =24a(11) =-6a(12) =-2a(13) =-3a(14) =-13a(15) =120a(16) =-24a(17) =-6a(18) =-6a(19) =-13a(20) =-71a(21) =720a(22) =-120a(23) =-24a(24) =-18a(25) =-26a(26) =-71a(27) =-461a(28) =5040a(29) =-720