T(n,k) = Number of lower triangles of an n X n -k..k array with all row and column sums zero.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =3a(6) =1a(7) =1a(8) =5a(9) =15a(10) =1a(11) =1a(12) =7a(13) =65a(14) =199a(15) =1a(16) =1a(17) =9a(18) =175a(19) =3753a(20) =6247a(21) =1a(22) =1a(23) =11a(24) =369a(25) =27267a(26) =860017a(27) =505623a(28) =1a(29) =1