T(n,k)=Number of n X n 0..k arrays with rows and columns in lexicographically nondecreasing order.

Terms

a(0) =2a(1) =3a(2) =7a(3) =4a(4) =29a(5) =45a(6) =5a(7) =86a(8) =1169a(9) =650a(10) =6a(11) =205a(12) =14178a(13) =250841a(14) =24520a(15) =7a(16) =421a(17) =102251a(18) =21907055a(19) =318174607a(20) =2625117a(21) =8a(22) =777a(23) =520017a(24) =733861607a(25) =348053502590a(27) =836488618a(28) =9a(29) =1324a(30) =2066505