T(n,k) = [n/2]!*[(n+1)/2]!*C([n/2],k-1)*C([(n+1)/2],k-1) where [x] = floor(x).

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =2a(6) =0a(7) =0a(8) =4a(9) =4a(10) =0a(11) =0a(12) =0a(13) =16a(14) =12a(15) =0a(16) =0a(17) =0a(18) =4a(19) =72a(20) =36a(21) =0a(22) =0a(23) =0a(24) =0a(25) =36a(26) =324a(27) =144a(28) =0a(29) =0