Table read by antidiagonals: T(n,k) = number of labeled partitions of (n,k) into pairs (i,j).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =3a(5) =1a(6) =1a(7) =7a(8) =7a(9) =1a(10) =1a(11) =15a(12) =25a(13) =15a(14) =1a(15) =1a(16) =31a(17) =79a(18) =79a(19) =31a(20) =1a(21) =1a(22) =63a(23) =241a(24) =339a(25) =241a(26) =63a(27) =1a(28) =1a(29) =127