cp's OEIS Frontend

A326960 Number of sets of subsets of {1..n} covering all n vertices whose dual is a (strict) antichain, also called covering T_1 sets of subsets.

%I A326960 #9 Aug 13 2019 13:19:38
%S A326960 2,2,4,72,38040,4020463392,18438434825136728352,
%T A326960 340282363593610211921722192165556850240,
%U A326960 115792089237316195072053288318104625954343609704705784618785209431974668731584
%N A326960 Number of sets of subsets of {1..n} covering all n vertices whose dual is a (strict) antichain, also called covering T_1 sets of subsets.
%C A326960 Same as A059052 except with a(1) = 2 instead of 4.
%C A326960 The dual of a set of subsets 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 of subsets where no edge is a subset of any other.
%C A326960 Alternatively, these are sets of subsets of {1..n} covering all n vertices where every vertex is the unique common element of some subset of the edges.
%F A326960 Binomial transform of A326967.
%e A326960 The a(0) = 2 through a(2) = 4 sets of subsets:
%e A326960   {}    {{1}}     {{1},{2}}
%e A326960   {{}}  {{},{1}}  {{},{1},{2}}
%e A326960                   {{1},{2},{1,2}}
%e A326960                   {{},{1},{2},{1,2}}
%t A326960 Table[Length[Select[Subsets[Subsets[Range[n]]],Length[Union[Select[Intersection@@@Rest[Subsets[#]],Length[#]==1&]]]==n&]],{n,0,3}]
%Y A326960 Covering sets of subsets are A000371.
%Y A326960 Covering T_0 sets of subsets are A326939.
%Y A326960 The case without empty edges is A326961.
%Y A326960 The non-covering version is A326967.
%Y A326960 Cf. A003181, A059052, A059523, A319639, A326951, A326965, A326974, A326976, A326977, A326979.
%K A326960 nonn
%O A326960 0,1
%A A326960 _Gus Wiseman_, Aug 13 2019