T(n,k) = number of n X n 0..k zero-diagonal arrays with corresponding row and column sums equal.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =10a(6) =1a(7) =4a(8) =45a(9) =152a(10) =1a(11) =5a(12) =136a(13) =4743a(14) =7736a(15) =1a(16) =6a(17) =325a(18) =59008a(19) =3801411a(20) =1375952a(21) =1a(22) =7a(23) =666a(24) =426425a(25) =345706336a(26) =23938685973a(27) =877901648a(28) =1a(29) =8