T(n,k) = Number of n X k arrays containing k copies of 0..n-1 with row sums equal.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =4a(5) =0a(6) =1a(7) =0a(8) =12a(9) =0a(10) =1a(11) =36a(12) =216a(13) =96a(14) =0a(15) =1a(16) =0a(17) =2700a(18) =0a(19) =480a(20) =0a(21) =1a(22) =400a(23) =54000a(24) =643680a(25) =116640a(26) =5760a(27) =0a(28) =1a(29) =0