cp's OEIS Frontend

A326939 Number of T_0 sets of subsets of {1..n} that cover all n vertices.

%I A326939 #10 Aug 09 2019 07:16:37
%S A326939 2,2,8,192,63384,4294003272,18446743983526539408,
%T A326939 340282366920938462946865774750753349904,
%U A326939 115792089237316195423570985008687907841019819456486779364848020385134373080448
%N A326939 Number of T_0 sets of subsets of {1..n} that cover all n vertices.
%C A326939 The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. 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 A326939 a(n) = 2 * A059201(n).
%F A326939 Inverse binomial transform of A326941.
%e A326939 The a(0) = 2 through a(2) = 8 sets of subsets:
%e A326939   {}    {{1}}     {{1},{2}}
%e A326939   {{}}  {{},{1}}  {{1},{1,2}}
%e A326939                   {{2},{1,2}}
%e A326939                   {{},{1},{2}}
%e A326939                   {{},{1},{1,2}}
%e A326939                   {{},{2},{1,2}}
%e A326939                   {{1},{2},{1,2}}
%e A326939                   {{},{1},{2},{1,2}}
%t A326939 dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];
%t A326939 Table[Length[Select[Subsets[Subsets[Range[n]]],Union@@#==Range[n]&&UnsameQ@@dual[#]&]],{n,0,3}]
%Y A326939 The non-T_0 version is A000371.
%Y A326939 The case without empty edges is A059201.
%Y A326939 The non-covering version is A326941.
%Y A326939 The unlabeled version is A326942.
%Y A326939 The case closed under intersection is A326943.
%Y A326939 Cf. A003180, A003181, A003465, A316978, A319564, A319637, A326940, A326947.
%K A326939 nonn
%O A326939 0,1
%A A326939 _Gus Wiseman_, Aug 07 2019