T(n,k) = binomial(n,k)*A000111(n-k)*(-1)^(n-k), 0 <= k <= n.

Terms

a(0) =1a(1) =-1a(2) =1a(3) =1a(4) =-2a(5) =1a(6) =-2a(7) =3a(8) =-3a(9) =1a(10) =5a(11) =-8a(12) =6a(13) =-4a(14) =1a(15) =-16a(16) =25a(17) =-20a(18) =10a(19) =-5a(20) =1a(21) =61a(22) =-96a(23) =75a(24) =-40a(25) =15a(26) =-6a(27) =1a(28) =-272a(29) =427