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Search: id:A020555
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| A020555 |
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Number of multigraphs on n labeled edges (with loops). Also number of genetically distinct states amongst n individuals. |
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+0
5
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| 1, 2, 9, 66, 712, 10457, 198091, 4659138, 132315780, 4441561814, 173290498279, 7751828612725, 393110572846777, 22385579339430539, 1419799938299929267, 99593312799819072788, 7678949893962472351181
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also the number of factorizations of (p_n#)^2. - David W. Wilson (davidwwilson(AT)comcast.net), Apr 30, 2001
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REFERENCES
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G. Labelle, Counting enriched multigraphs..., Discrete Math., 217 (2000), 237-248.
E. Keith Lloyd (ekl(AT)soton.ac.uk), Math. Proc. Camb. Phil. Soc., vol. 103 (1988), 277-284.
A. Murthy, Generalization of partition function, introducing Smarandache factor partitions. Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000.
A. Murthy, Program for finding out the number of Smarandache factor partitions. (To be published in Smarandache Notions Journal).
G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Math. Dept., Univ. Qu\'ebec \`a Montr\'eal, 2004.
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LINKS
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M. L. Perez et al., eds., Smarandache Notions Journal
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FORMULA
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Lloyd's article gives a complicated explicit formula.
E.g.f.: exp(-3/2+exp(x)/2)*Sum(exp(binomial(n+1, 2)*x)/n!, n=0..infinity) [probably in the Labelle paper] - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 27 2004
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CROSSREFS
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Cf. A020554, A014500, A014501.
Sequence in context: A152213 A089471 A118804 this_sequence A091795 A158952 A120020
Adjacent sequences: A020552 A020553 A020554 this_sequence A020556 A020557 A020558
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KEYWORD
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nonn
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AUTHOR
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Gilbert Labelle (gilbert(AT)lacim.uqam.ca), Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).
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