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

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =2a(5) =24a(6) =0a(7) =2a(8) =120a(9) =720a(10) =0a(11) =2a(12) =504a(13) =10080a(14) =40320a(15) =0a(16) =2a(17) =2040a(18) =105840a(19) =1209600a(20) =3628800a(21) =0a(22) =2a(23) =8184a(24) =1013760a(25) =25280640a(26) =199584000a(27) =479001600a(28) =0a(29) =2