Triangle read by rows: T(n,k) = Sum_{j=0..k} (-1)^j * binomial(k,j) * (2-j)^n.

Terms

a(0) =1a(1) =2a(2) =1a(3) =4a(4) =3a(5) =2a(6) =8a(7) =7a(8) =6a(9) =6a(10) =16a(11) =15a(12) =14a(13) =12a(14) =24a(15) =32a(16) =31a(17) =30a(18) =30a(19) =0a(20) =120a(21) =64a(22) =63a(23) =62a(24) =60a(25) =120a(26) =-360a(27) =720a(28) =128a(29) =127