# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a326950 Showing 1-1 of 1 %I A326950 #20 Jun 02 2023 01:13:48 %S A326950 1,2,4,12,107,6439,7726965,2414519001532,56130437161079183223017, %T A326950 286386577668298409107773412840148848120595 %N A326950 Number of T_0 antichains of nonempty subsets of {1..n}. %C A326950 The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges). %F A326950 Binomial transform of A245567, if we assume A245567(0) = 1. %e A326950 The a(0) = 1 through a(3) = 12 antichains: %e A326950 {} {} {} {} %e A326950 {{1}} {{1}} {{1}} %e A326950 {{2}} {{2}} %e A326950 {{1},{2}} {{3}} %e A326950 {{1},{2}} %e A326950 {{1},{3}} %e A326950 {{2},{3}} %e A326950 {{1,2},{1,3}} %e A326950 {{1,2},{2,3}} %e A326950 {{1},{2},{3}} %e A326950 {{1,3},{2,3}} %e A326950 {{1,2},{1,3},{2,3}} %t A326950 dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}]; %t A326950 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}]; %t A326950 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],stableQ[#,SubsetQ]&&UnsameQ@@dual[#]&]],{n,0,3}] %Y A326950 Antichains of nonempty sets are A014466. %Y A326950 T_0 set-systems are A326940. %Y A326950 The covering case is A245567. %Y A326950 Cf. A006126, A059201, A059052, A245567, A319559, A319564, A326030, A326946, A326947. %K A326950 nonn,more %O A326950 0,2 %A A326950 _Gus Wiseman_, Aug 08 2019 %E A326950 a(5)-a(8) from _Andrew Howroyd_, Aug 14 2019 %E A326950 a(9), based on A245567, from _Patrick De Causmaecker_, Jun 01 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE