%N Number of labeled simple connected graphs covering n vertices with at least one bridge that is not an endpoint/leaf (non-spanning edge-connectivity 1).
%C A bridge is an edge that, if removed without removing any incident vertices, disconnects the graph. Graphs with no bridges are counted by A095983 (2-edge-connected graphs).
%C Also labeled simple connected graphs covering n vertices with non-spanning edge-connectivity 1, where the non-spanning edge-connectivity of a graph is the minimum number of edges that must be removed (along with any non-covered vertices) to obtain a disconnected or empty graph.
%F a(n) = A001187(n) - A322395(n) for n > 2. - _Andrew Howroyd_, Aug 27 2019
%F Inverse binomial transform of A327231.
%Y Column k = 1 of A327149.
%Y The non-covering version is A327231.
%Y Connected bridged graphs (spanning edge-connectivity 1) are A327071.
%Y BII-numbers of graphs with non-spanning edge-connectivity 1 are A327099.
%Y Covering set-systems with non-spanning edge-connectivity 1 are A327129.
%Y Cf. A001187, A006129, A052446, A059166, A322395, A327072, A327073, A327148.
%A _Gus Wiseman_, Aug 25 2019
%E Terms a(6) and beyond from _Andrew Howroyd_, Aug 27 2019