|
Search: id:A137916
|
|
|
| A137916 |
|
Number of labeled graphs on [n] with unicyclic components. |
|
+0
2
|
|
| 0, 0, 1, 15, 222, 3670, 68820, 1456875, 34506640, 906073524, 26154657270, 823808845585, 28129686128940, 1035350305641990, 40871383866109888, 1722832666898627865, 77242791668604946560, 3670690919234354407000
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
The first values are row sums of A106239.
|
|
LINKS
|
Wikipedia, Pseudo forest
|
|
FORMULA
|
a(n)= Sum N/D over the partitions of n: 1p_1+2p_2+ ... +np_n, with parts >=3, where N = n!*product_{1=<i<=n}= A057500(i)^p_i, and D = product_{1=<i<=n}(p_i!(i!)^p_i).
|
|
EXAMPLE
|
E.g. a(6) = 3670 because there are 3660 distinct labeled unicycles with 6 vertices, and only 10 ways to label two triangles.
|
|
CROSSREFS
|
Cf. A057500, A106239.
Sequence in context: A027843 A027840 A057500 this_sequence A078364 A012852 A001024
Adjacent sequences: A137913 A137914 A137915 this_sequence A137917 A137918 A137919
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Washington G. Bomfim (webonfim(AT)bol.com.br), Feb 22 2008
|
|
|
Search completed in 0.002 seconds
|
