T(n,k) = number of n X k 0..k-1 arrays with no column j greater than column j-1 in all rows.

Terms

a(0) =1a(1) =3a(2) =1a(3) =10a(4) =15a(5) =1a(6) =35a(7) =568a(8) =63a(9) =1a(10) =126a(11) =39695a(12) =18226a(13) =255a(14) =1a(15) =462a(16) =4431876a(17) =14177855a(18) =518320a(19) =1023a(20) =1a(21) =1716a(22) =724082352a(23) =23124921876a(24) =4041974015a(25) =14230810a(26) =4095a(27) =1a(28) =6435a(29) =163050236504