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Search: id:A002807
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| A002807 |
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Sum_{k=3..n} (k-1)!*C(n,k)/2.
(Formerly M4420 N1867)
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+0
6
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| 0, 0, 0, 1, 7, 37, 197, 1172, 8018, 62814, 556014, 5488059, 59740609, 710771275, 9174170011, 127661752406, 1904975488436, 30341995265036, 513771331467372, 9215499383109573, 174548332364311563, 3481204991988351553, 72920994844093191553, 1600596371590399671784
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Maximal number of cycles in complete graph on n nodes. - Erich Friedman (erich.friedman(AT)stetson.edu).
Number of equations that must be checked to verify reversibility of an n state Markov chain using the Kolmogorov criterion [From Qian Jiang (jiang1h(AT)uwindsor.ca), Jun 08 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. P. Char, Master circuit matrix, Proc. IEE, 115 (1968), 762-770.
F. C. Holroyd and W. J. G. Wingate, Cycles in the complement of a tree or other graph, Discrete Math., 55 (1985), 267-282.
E.P.C. Kao, An Introduction to Stochastic Processes, Duxbury Press, 1997, 209-210. [From Qian Jiang (jiang1h(AT)uwindsor.ca), Jun 08 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, ch. 7.
Eric Weisstein's World of Mathematics, Complete Graph
Eric Weisstein's World of Mathematics, Graph Cycle
M. Scullard, Reversible Markov Chains [From Qian Jiang (jiang1h(AT)uwindsor.ca), Jun 08 2009]
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FORMULA
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E.g.f.: (-1/4)*exp(x)*(2*ln(1-x)+2*x+x^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 26 2004
a(n)=(n-1)*(n-2)/2+n*a(n-1)-(n-1)*a(n-2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 22 2005
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CROSSREFS
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Cf. A117130, A099198, A099201, A070968.
Sequence in context: A085640 A069378 A117130 this_sequence A124610 A002683 A126475
Adjacent sequences: A002804 A002805 A002806 this_sequence A002808 A002809 A002810
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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