T(n, k) is the number of k-element connected subposets of the n-th Boolean lattice, 0 <= k <= 2^n.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =1a(5) =1a(6) =4a(7) =5a(8) =4a(9) =1a(10) =1a(11) =8a(12) =19a(13) =42a(14) =61a(15) =56a(16) =28a(17) =8a(18) =1a(19) =1a(20) =16a(21) =65a(22) =304a(23) =1129a(24) =3200a(25) =6775a(26) =10680a(27) =12600a(28) =11386a(29) =8002