T(n,k)=Number of nXk 0..3 arrays with the row and column sums nondecreasing.

Terms

a(0) =4a(1) =10a(2) =10a(3) =20a(4) =90a(5) =20a(6) =35a(7) =616a(8) =616a(9) =35a(10) =56a(11) =3731a(12) =15688a(13) =3731a(14) =56a(15) =84a(16) =20208a(17) =343827a(18) =343827a(19) =20208a(20) =84a(21) =120a(22) =102665a(23) =6776376a(24) =27871870a(25) =6776376a(26) =102665a(27) =120a(28) =165a(29) =492118