T(n,k) is the number of n X n 0..k arrays with row and column sums equal.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =1a(6) =1a(7) =3a(8) =4a(9) =1a(10) =1a(11) =4a(12) =9a(13) =14a(14) =1a(15) =1a(16) =5a(17) =16a(18) =87a(19) =140a(20) =1a(21) =1a(22) =6a(23) =25a(24) =340a(25) =5673a(26) =4322a(27) =1a(28) =1a(29) =7