%I #9 Oct 28 2023 14:56:41
%S 1,0,1,4,41,3048,26894637
%N Number of unlabeled connectedness systems covering n vertices without singletons.
%C 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.
%e Non-isomorphic representatives of the a(3) = 4 connectedness systems:
%e {{1,2,3}}
%e {{2,3},{1,2,3}}
%e {{1,3},{2,3},{1,2,3}}
%e {{1,2},{1,3},{2,3},{1,2,3}}
%Y The case with singletons is A326871.
%Y First differences of A072444 (the non-covering case).
%Y Euler transform of A072445 (the connected case).
%Y The labeled version is A326877.
%Y Cf. A072446, A072447, A193674, A323818, A326866, A326867, A326868, A326869, A326870.
%K nonn,more
%O 0,4
%A _Gus Wiseman_, Aug 02 2019
%E a(6) corrected by _Andrew Howroyd_, Oct 28 2023