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 A326945 #9 Aug 15 2019 15:29:52
%S A326945 2,4,12,96,4404,2725942,151906396568,28175293281055562650
%N A326945 Number of T_0 sets of subsets of {1..n} that are closed under intersection.
%C A326945 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 A326945 Binomial transform of A326943.
%e A326945 The a(0) = 2 through a(2) = 12 sets of subsets:
%e A326945 {} {} {}
%e A326945 {{}} {{}} {{}}
%e A326945 {{1}} {{1}}
%e A326945 {{},{1}} {{2}}
%e A326945 {{},{1}}
%e A326945 {{},{2}}
%e A326945 {{1},{1,2}}
%e A326945 {{2},{1,2}}
%e A326945 {{},{1},{2}}
%e A326945 {{},{1},{1,2}}
%e A326945 {{},{2},{1,2}}
%e A326945 {{},{1},{2},{1,2}}
%t A326945 Table[Length[Select[Subsets[Subsets[Range[n]]],UnsameQ@@dual[#]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}]
%Y A326945 The non-T_0 version is A102897.
%Y A326945 The version not closed under intersection is A326941.
%Y A326945 The covering case is A326943.
%Y A326945 The case without empty edges is A326959.
%Y A326945 Cf. A003180, A182507, A316978, A319564, A326906, A326939, A326940, A326944, A326947.
%K A326945 nonn,more
%O A326945 0,1
%A A326945 _Gus Wiseman_, Aug 08 2019
%E A326945 a(5)-a(7) from _Andrew Howroyd_, Aug 14 2019