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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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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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
| 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]
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, ch. 7. [?Broken link]
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, ch. 7.
M. Scullard, Reversible Markov Chains [From Qian Jiang (jiang1h(AT)uwindsor.ca), Jun 08 2009]
Eric Weisstein's World of Mathematics, Complete Graph
Eric Weisstein's World of Mathematics, Graph Cycle
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FORMULA
| 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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MATHEMATICA
| Table[Sum[((k-1)!Binomial[n, k])/2, {k, 3, n}], {n, 0, 25}] (* From Harvey P. Dale, June 24 2011 *)
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CROSSREFS
| Cf. A117130, A099198, A099201, A070968.
Sequence in context: A196805 A069378 A117130 * A124610 A002683 A126475
Adjacent sequences: A002804 A002805 A002806 * A002808 A002809 A002810
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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