T(n,k)=Number of nXk 0..2 arrays with the row and column sums nondecreasing.

Terms

a(0) =3a(1) =6a(2) =6a(3) =10a(4) =32a(5) =10a(6) =15a(7) =133a(8) =133a(9) =15a(10) =21a(11) =510a(12) =1510a(13) =510a(14) =21a(15) =28a(16) =1792a(17) =15300a(18) =15300a(19) =1792a(20) =28a(21) =36a(22) =6050a(23) =143690a(24) =423595a(25) =143690a(26) =6050a(27) =36a(28) =45a(29) =19641