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%I A306003 #15 Dec 21 2022 04:47:57
%S A306003 0,0,1,4,18,107,846,11122,261212,11717906,1006716728,164060156360,
%T A306003 50335920919080,29003488522658695,31397381311096116107,
%U A306003 63969560164236980493127,245871831711291931225960094,1787331725280413408599670721723,24636021429463963332562215579906526
%N A306003 Number of simple graphs on n nodes where each component has at least one cycle.
%C A306003 Euler transform of A241841. Here the graphs are simple (no loops, no multi-edges) but not necessarily connected.
%H A306003 Georg Fischer, <a href="/A306003/b306003.txt">Table of n, a(n) for n = 1..40</a>
%e A306003 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 A306003 a(8) = 11122 counts A241841(8) = 11094 graphs with one component and 28 graphs with two components.
%e A306003 a(9) = 261212 counts A241841(9) = 261033 graphs with one component, 178 graphs with two components, and 1 graph with 3 components.
%Y A306003 Cf. A241841 (connected variant), A286743 (at least one component has one cycle).
%K A306003 nonn
%O A306003 1,4
%A A306003 _R. J. Mathar_, Jun 16 2018
%E A306003 a(19) corrected by _Georg Fischer_, Dec 20 2022

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