T(n,k) is the number of connected labeled posets with n elements and rank k: triangle read by rows.

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =6a(5) =6a(6) =0a(7) =38a(8) =84a(9) =24a(10) =0a(11) =390a(12) =1710a(13) =840a(14) =120a(15) =0a(16) =6062a(17) =49740a(18) =36840a(19) =8280a(20) =720a(21) =0a(22) =134526a(23) =2050566a(24) =2184000a(25) =646800a(26) =85680a(27) =5040a(28) =0a(29) =4172198