Triangle T(n,k) of number of chains of length k in partitions of an n-set ordered by refinement.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =2a(5) =1a(6) =0a(7) =5a(8) =7a(9) =3a(10) =0a(11) =15a(12) =45a(13) =49a(14) =18a(15) =0a(16) =52a(17) =306a(18) =640a(19) =565a(20) =180a(21) =0a(22) =203a(23) =2268a(24) =8176a(25) =13055a(26) =9645a(27) =2700a(28) =0a(29) =877