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 A326871 #24 Jan 18 2024 04:41:35
%S A326871 1,1,4,24,436,80460,1689114556
%N A326871 Number of unlabeled connectedness systems covering n vertices.
%C A326871 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.
%e A326871 Non-isomorphic representatives of the a(0) = 1 through a(3) = 24 connectedness systems:
%e A326871 {} {{1}} {{1,2}} {{1,2,3}}
%e A326871 {{1},{2}} {{1},{2,3}}
%e A326871 {{2},{1,2}} {{1},{2},{3}}
%e A326871 {{1},{2},{1,2}} {{3},{1,2,3}}
%e A326871 {{1},{3},{2,3}}
%e A326871 {{2,3},{1,2,3}}
%e A326871 {{2},{3},{1,2,3}}
%e A326871 {{1},{2,3},{1,2,3}}
%e A326871 {{1},{2},{3},{2,3}}
%e A326871 {{3},{2,3},{1,2,3}}
%e A326871 {{1},{2},{3},{1,2,3}}
%e A326871 {{1,3},{2,3},{1,2,3}}
%e A326871 {{1},{3},{2,3},{1,2,3}}
%e A326871 {{2},{3},{2,3},{1,2,3}}
%e A326871 {{2},{1,3},{2,3},{1,2,3}}
%e A326871 {{3},{1,3},{2,3},{1,2,3}}
%e A326871 {{1,2},{1,3},{2,3},{1,2,3}}
%e A326871 {{1},{2},{3},{2,3},{1,2,3}}
%e A326871 {{1},{2},{1,3},{2,3},{1,2,3}}
%e A326871 {{2},{3},{1,3},{2,3},{1,2,3}}
%e A326871 {{3},{1,2},{1,3},{2,3},{1,2,3}}
%e A326871 {{1},{2},{3},{1,3},{2,3},{1,2,3}}
%e A326871 {{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%e A326871 {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%Y A326871 The non-covering case without singletons is A072444.
%Y A326871 The case without singletons is A326899.
%Y A326871 First differences of A326867 (the non-covering case).
%Y A326871 Euler transform of A326869 (the connected case).
%Y A326871 The labeled case is A326870.
%Y A326871 Cf. A072445, A072446, A072447, A193674, A323818, A326866, A326868.
%K A326871 nonn,more
%O A326871 0,3
%A A326871 _Gus Wiseman_, Jul 29 2019
%E A326871 a(5) from _Andrew Howroyd_, Aug 10 2019
%E A326871 a(6) from _Andrew Howroyd_, Oct 28 2023