T(n,k)=Number of n X n 0..k matrices with row and column i=1..n having sum <= i*k.

Terms

a(0) =2a(1) =3a(2) =10a(3) =4a(4) =42a(5) =138a(6) =5a(7) =120a(8) =3186a(9) =5314a(10) =6a(11) =275a(12) =32060a(13) =1299735a(14) =575122a(15) =7a(16) =546a(17) =199735a(18) =74323976a(19) =2860343784a(20) =176041978a(21) =8a(22) =980a(23) =909900a(24) =1839121115a(27) =153143689594a(28) =9a(29) =1632a(30) =3323712a(31) =26346319032