Array giving number of (k,2)-noncrossing partitions of [n], read by antidiagonals.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =1a(7) =1a(8) =2a(9) =5a(10) =1a(11) =1a(12) =2a(13) =5a(14) =14a(15) =1a(16) =1a(17) =2a(18) =5a(19) =15a(20) =42a(21) =1a(22) =1a(23) =2a(24) =5a(25) =15a(26) =51a(27) =132a(28) =1a(29) =1