T(n,k)=Number of n X n 0..k symmetric arrays with every row summing to floor(n*k/2).

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =4a(6) =1a(7) =4a(8) =13a(9) =18a(10) =1a(11) =5a(12) =29a(13) =169a(14) =112a(15) =1a(16) =6a(17) =57a(18) =880a(19) =5673a(20) =1760a(21) =1a(22) =7a(23) =96a(24) =3249a(25) =87932a(26) =526443a(27) =35150a(28) =1a(29) =8