%I
%S 1,1,0,1,2,3,8,17,41,103,276
%N Number of nonisomorphic connected T_0 set systems of weight n.
%C 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 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 Nonisomorphic representatives of the a(1) = 1 through a(6) = 8 set systems:
%e 1: {{1}}
%e 3: {{2},{1,2}}
%e 4: {{1,3},{2,3}}
%e {{1},{2},{1,2}}
%e 5: {{2},{3},{1,2,3}}
%e {{2},{1,3},{2,3}}
%e {{3},{1,3},{2,3}}
%e 6: {{3},{1,4},{2,3,4}}
%e {{3},{2,3},{1,2,3}}
%e {{1,2},{1,3},{2,3}}
%e {{1,3},{2,4},{3,4}}
%e {{1,4},{2,4},{3,4}}
%e {{1},{2},{3},{1,2,3}}
%e {{1},{2},{1,3},{2,3}}
%e {{2},{3},{1,3},{2,3}}
%Y Cf. A007716, A007718, A049311, A056156, A059201, A283877, A316980.
%Y Cf. A319557, A319558, A319559, A319560, A319564, A319565, A319567.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, Sep 23 2018
