T(n,k) = number of n X k 0..1 arrays with rows unimodal and columns nondecreasing.

Terms

a(0) =2a(1) =4a(2) =3a(3) =7a(4) =9a(5) =4a(6) =11a(7) =22a(8) =16a(9) =5a(10) =16a(11) =46a(12) =50a(13) =25a(14) =6a(15) =22a(16) =86a(17) =130a(18) =95a(19) =36a(20) =7a(21) =29a(22) =148a(23) =296a(24) =295a(25) =161a(26) =49a(27) =8a(28) =37a(29) =239