Table by antidiagonals of T(n,k)=n*T(n,k-1)-T(n,k-2) starting with T(n,1)=1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =0a(4) =2a(5) =1a(6) =-1a(7) =3a(8) =3a(9) =1a(10) =-1a(11) =4a(12) =8a(13) =4a(14) =1a(15) =0a(16) =5a(17) =21a(18) =15a(19) =5a(20) =1a(21) =1a(22) =6a(23) =55a(24) =56a(25) =24a(26) =6a(27) =1a(28) =1a(29) =7