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 A326870 #11 Oct 28 2023 12:49:04
%S A326870 1,1,5,77,6377,8097721,1196051135917
%N A326870 Number of connectedness systems covering n vertices.
%C A326870 We define a connectedness system (investigated by Vim van Dam in 2002) to be a set of finite nonempty sets (edges) that is closed under taking the union of any two overlapping edges. It is covering if every vertex belongs to some edge.
%H A326870 Gus Wiseman, <a href="http://www.mathematica-journal.com/2017/12/every-clutter-is-a-tree-of-blobs/">Every Clutter Is a Tree of Blobs</a>, The Mathematica Journal, Vol. 19, 2017.
%e A326870 The a(2) = 5 connectedness systems:
%e A326870 {{1,2}}
%e A326870 {{1},{2}}
%e A326870 {{1},{1,2}}
%e A326870 {{2},{1,2}}
%e A326870 {{1},{2},{1,2}}
%t A326870 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Union@@#==Range[n]&&SubsetQ[#,Union@@@Select[Tuples[#,2],Intersection@@#!={}&]]&]],{n,0,4}]
%Y A326870 Inverse binomial transform of A326866 (the non-covering case).
%Y A326870 Exponential transform of A326868 (the connected case).
%Y A326870 The unlabeled case is A326871.
%Y A326870 The BII-numbers of these set-systems are A326872.
%Y A326870 The case without singletons is A326877.
%Y A326870 Cf. A072445, A072446, A072447, A102896, A323818, A326867, A326869.
%K A326870 nonn,more
%O A326870 0,3
%A A326870 _Gus Wiseman_, Jul 29 2019
%E A326870 a(6) corrected by _Christian Sievers_, Oct 28 2023