cp's OEIS Frontend

A326965 Number of set-systems on n vertices where every covered vertex is the unique common element of some subset of the edges.

%I A326965 #8 Aug 12 2019 22:31:45
%S A326965 1,2,5,46,19181,2010327182,9219217424630040409,
%T A326965 170141181796805106025395618012972506978,
%U A326965 57896044618658097536026644159052312978532934306727333157337631572314050272137
%N A326965 Number of set-systems on n vertices where every covered vertex is the unique common element of some subset of the edges.
%C A326965 A set-system is a finite set of finite nonempty sets. 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}}. An antichain is a set-system where no edge is a subset of any other. This sequence counts set-systems whose dual is a (strict) antichain, also called T_1 set-systems.
%F A326965 Binomial transform of A326961.
%F A326965 a(n) = A326967(n)/2.
%e A326965 The a(0) = 1 through a(2) = 5 set-systems:
%e A326965   {}  {}     {}
%e A326965       {{1}}  {{1}}
%e A326965              {{2}}
%e A326965              {{1},{2}}
%e A326965              {{1},{2},{1,2}}
%t A326965 tmQ[eds_]:=Union@@Select[Intersection@@@Rest[Subsets[eds]],Length[#]==1&]==Union@@eds;
%t A326965 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],tmQ]],{n,0,3}]
%Y A326965 Set-systems are A058891.
%Y A326965 T_0 set-systems are A326940.
%Y A326965 The covering case is A326961.
%Y A326965 The version with empty edges allowed is A326967.
%Y A326965 Set-systems whose dual is a weak antichain are A326968.
%Y A326965 The unlabeled version is A326972.
%Y A326965 The BII_numbers of these set-systems are A326979.
%Y A326965 Cf. A059052, A326951, A326966, A326970, A326971, A326976, A326977.
%K A326965 nonn
%O A326965 0,2
%A A326965 _Gus Wiseman_, Aug 10 2019