%N Number of simple graphs on n nodes where each component has at least one cycle.
%C Euler transform of A241841. Here the graphs are simple (no loops, no multi-edges) but not necessarily connected.
%e a(7)=846 counts A241841(7)=842 graphs with one component plus 4 graphs with two components (the two components being the connected graph on 3 nodes and any of the 4 graphs on 4 nodes).
%e a(8) = 11122 counts A241841(8) = 11094 graphs with one component and 28 graphs with two components.
%e a(9) = 261212 counts A241841(9) = 261033 graphs with one component, 178 graphs with two components, and 1 graph with 3 components.
%Y Cf. A241841 (connected variant), A286743 (at least one component has one cycle).
%A _R. J. Mathar_, Jun 16 2018