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 A319559 #11 May 04 2025 15:37:29
%S A319559 1,1,1,2,4,7,16,35,82,200,517,1373,3867,11216,33910,105950
%N A319559 Number of non-isomorphic T_0 set systems of weight n.
%C A319559 In a set system, two vertices are equivalent if in every block the presence of the first is equivalent to the presence of the second. The T_0 condition means that there are no equivalent vertices.
%C A319559 The weight of a set system is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%e A319559 Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems:
%e A319559 1: {{1}}
%e A319559 2: {{1},{2}}
%e A319559 3: {{2},{1,2}}
%e A319559 {{1},{2},{3}}
%e A319559 4: {{1,3},{2,3}}
%e A319559 {{1},{2},{1,2}}
%e A319559 {{1},{3},{2,3}}
%e A319559 {{1},{2},{3},{4}}
%e A319559 5: {{1},{2,4},{3,4}}
%e A319559 {{2},{3},{1,2,3}}
%e A319559 {{2},{1,3},{2,3}}
%e A319559 {{3},{1,3},{2,3}}
%e A319559 {{1},{2},{3},{2,3}}
%e A319559 {{1},{2},{4},{3,4}}
%e A319559 {{1},{2},{3},{4},{5}}
%Y A319559 Cf. A007716, A007718, A049311, A053419, A056156, A059201, A283877, A305854, A306006, A316980, A317757.
%Y A319559 Cf. A319557, A319558, A319560, A319564, A319565, A319566, A319567.
%K A319559 nonn,more
%O A319559 0,4
%A A319559 _Gus Wiseman_, Sep 23 2018
%E A319559 a(11)-a(15) from _Bert Dobbelaere_, May 04 2025