

A306003


Number of simple graphs on n nodes where each component has at least one cycle.


1



0, 0, 1, 4, 18, 107, 846, 11122, 261212, 11717906, 1006716728, 164060156360, 50335920919080, 29003488522658695, 31397381311096116107, 63969560164236980493127, 245871831711291931225960094, 1787331725280413408599670721723, 2463602142946396333256221557990652
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OFFSET

1,4


COMMENTS

Euler transform of A241841. Here the graphs are simple (no loops, no multiedges) but not necessarily connected.


LINKS

Table of n, a(n) for n=1..19.


EXAMPLE

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).
a(8) = 11122 counts A241841(8) = 11094 graphs with one component and 28 graphs with two components.
a(9) = 261212 counts A241841(9) = 261033 graphs with one component, 178 graphs with two components, and 1 graph with 3 components.


CROSSREFS

Cf. A241841 (connected variant), A286743 (at least one component has one cycle).
Sequence in context: A009597 A241841 A241842 * A214840 A060223 A144085
Adjacent sequences: A306000 A306001 A306002 * A306004 A306005 A306006


KEYWORD

nonn


AUTHOR

R. J. Mathar, Jun 16 2018


STATUS

approved



