cp's OEIS Frontend

A326941 Number of T_0 sets of subsets of {1..n}.

%I A326941 #8 Aug 15 2019 15:38:56
%S A326941 2,4,14,224,64210,4294322204,18446744009291513774,
%T A326941 340282366920938463075992982725615419816,
%U A326941 115792089237316195423570985008687907843742078391854287068939455414919611614210
%N A326941 Number of T_0 sets of subsets of {1..n}.
%C A326941 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 A326941 a(n) = 2 * A326940(n).
%F A326941 Binomial transform of A326939.
%e A326941 The a(0) = 2 through a(2) = 14 sets of subsets:
%e A326941   {}    {}        {}
%e A326941   {{}}  {{}}      {{}}
%e A326941         {{1}}     {{1}}
%e A326941         {{},{1}}  {{2}}
%e A326941                   {{},{1}}
%e A326941                   {{},{2}}
%e A326941                   {{1},{2}}
%e A326941                   {{1},{1,2}}
%e A326941                   {{2},{1,2}}
%e A326941                   {{},{1},{2}}
%e A326941                   {{},{1},{1,2}}
%e A326941                   {{},{2},{1,2}}
%e A326941                   {{1},{2},{1,2}}
%e A326941                   {{},{1},{2},{1,2}}
%t A326941 dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];
%t A326941 Table[Length[Select[Subsets[Subsets[Range[n]]],UnsameQ@@dual[#]&]],{n,0,3}]
%Y A326941 The non-T_0 version is A001146.
%Y A326941 The covering case is A326939.
%Y A326941 The case without empty edges is A326940.
%Y A326941 The unlabeled version is A326949.
%Y A326941 Cf. A003180, A059201, A316978, A319559, A319564, A319637, A326946, A326947.
%K A326941 nonn
%O A326941 0,1
%A A326941 _Gus Wiseman_, Aug 07 2019
%E A326941 a(5)-a(8) from _Andrew Howroyd_, Aug 14 2019