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A143900
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Number of simple graphs on n labeled nodes containing at least one cycle subgraph, also row sums of A143899.
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2
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0, 0, 0, 1, 26, 733, 29836, 2060191, 267873508, 68709450231, 35184166480296, 36028792251523289, 73786976171465003256, 302231454900131663566437, 2475880078570650265515241808, 40564819207303337099536803011071, 1329227995784915872766249150185503728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..50
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FORMULA
| a(n) = A006125(n)-A001858(n).
a(n) = Sum_{k=3..C(n,2)} A143899(n,k).
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EXAMPLE
| a(3) = 1, because 1 simple graph on 3 nodes with 3 edges contains a cycle subgraph:
..1-2..
..|/...
..3....
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MAPLE
| graphs:= n-> 2^binomial(n, 2): forests:= n-> add (add (binomial (m, j) *binomial (n-1, n-m-j) *n^(n-m-j) *(m+j)!/ (-2)^j/ m!, j=0..m), m=0..n): a:= n-> graphs(n) -forests(n): seq (a(n), n=0..18);
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CROSSREFS
| Row sums of A143899. Cf. A006125, A001858, A007318.
Sequence in context: A181227 A094738 A182612 * A180792 A091742 A160140
Adjacent sequences: A143897 A143898 A143899 * A143901 A143902 A143903
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 04 2008
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