T(n,k)=Number of n X n 0..k arrays with corresponding row and column sums equal.

Terms

a(0) =2a(1) =3a(2) =8a(3) =4a(4) =27a(5) =80a(6) =5a(7) =64a(8) =1215a(9) =2432a(10) =6a(11) =125a(12) =8704a(13) =384183a(14) =247552a(15) =7a(16) =216a(17) =40625a(18) =15106048a(19) =923742873a(20) =88060928a(21) =8a(22) =343a(23) =143856a(24) =266515625a(25) =354003288064a(27) =112371410944a(28) =9a(29) =512a(30) =420175