%I #15 Dec 21 2022 04:47:57

%S 0,0,1,4,18,107,846,11122,261212,11717906,1006716728,164060156360,

%T 50335920919080,29003488522658695,31397381311096116107,

%U 63969560164236980493127,245871831711291931225960094,1787331725280413408599670721723,24636021429463963332562215579906526

%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.

%H Georg Fischer, <a href="/A306003/b306003.txt">Table of n, a(n) for n = 1..40</a>

%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).

%K nonn

%O 1,4

%A _R. J. Mathar_, Jun 16 2018

%E a(19) corrected by _Georg Fischer_, Dec 20 2022