T(n,k) = Sum_{j=0..k} (k-j)^n * binomial(n,j).

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =6a(6) =0a(7) =1a(8) =11a(9) =54a(10) =0a(11) =1a(12) =20a(13) =151a(14) =680a(15) =0a(16) =1a(17) =37a(18) =413a(19) =2569a(20) =11000a(21) =0a(22) =1a(23) =70a(24) =1128a(25) =9450a(26) =52431a(27) =217392a(28) =0a(29) =1