This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326943 #12 Aug 15 2019 15:30:07
%S A326943 2,2,6,70,4078,2704780,151890105214,28175292217767880450
%N A326943 Number of T_0 sets of subsets of {1..n} that cover all n vertices and are closed under intersection.
%C A326943 The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks 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 A326943 Inverse binomial transform of A326945.
%F A326943 a(n) = Sum_{k=0..n} Stirling1(n,k)*A326906(k). - _Andrew Howroyd_, Aug 14 2019
%e A326943 The a(0) = 2 through a(3) = 6 sets of subsets:
%e A326943 {} {{1}} {{1},{1,2}}
%e A326943 {{}} {{},{1}} {{2},{1,2}}
%e A326943 {{},{1},{2}}
%e A326943 {{},{1},{1,2}}
%e A326943 {{},{2},{1,2}}
%e A326943 {{},{1},{2},{1,2}}
%t A326943 dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];
%t A326943 Table[Length[Select[Subsets[Subsets[Range[n]]],Union@@#==Range[n]&&UnsameQ@@dual[#]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}]
%Y A326943 The non-T_0 version is A326906.
%Y A326943 The case without empty edges is A309615.
%Y A326943 The non-covering version is A326945.
%Y A326943 The version not closed under intersection is A326939.
%Y A326943 Cf. A003180, A003181, A003465, A059052, A059201, A245567, A316978, A319564, A319637, A326940, A326941, A326942, A326947.
%K A326943 nonn,more
%O A326943 0,1
%A A326943 _Gus Wiseman_, Aug 08 2019
%E A326943 a(5)-a(7) from _Andrew Howroyd_, Aug 14 2019