Search: id:A002807
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%I A002807 M4420 N1867
%S A002807 0,0,0,1,7,37,197,1172,8018,62814,556014,5488059,59740609,710771275,9174170011,
%T A002807 127661752406,1904975488436,30341995265036,513771331467372,9215499383109573,
%U A002807 174548332364311563,3481204991988351553,72920994844093191553,1600596371590399671784
%N A002807 Sum_{k=3..n} (k-1)!*C(n,k)/2.
%C A002807 Maximal number of cycles in complete graph on n nodes. - Erich Friedman 
               (erich.friedman(AT)stetson.edu).
%C A002807 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]
%D A002807 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002807 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002807 J. P. Char, Master circuit matrix, Proc. IEE, 115 (1968), 762-770.
%D A002807 F. C. Holroyd and W. J. G. Wingate, Cycles in the complement of a tree 
               or other graph, Discrete Math., 55 (1985), 267-282.
%D A002807 E.P.C. Kao, An Introduction to Stochastic Processes, Duxbury Press, 1997, 
               209-210. [From Qian Jiang (jiang1h(AT)uwindsor.ca), Jun 08 2009]
%H A002807 T. D. Noe, <a href="b002807.txt">Table of n, a(n) for n=0..100</a>
%H A002807 P. Pollack, <a href="http://www.math.dartmouth.edu/~ppollack/notes.pdf">
               Analytic and Combinatorial Number Theory</a> Course Notes, ch. 7.
%H A002807 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CompleteGraph.html">Complete Graph</a>
%H A002807 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GraphCycle.html">Graph Cycle</a>
%H A002807 M. Scullard, <a href="http://www.math.ucsd.edu/~williams/courses/m28908/
               scullardMath289_Reversibility.pdf"> Reversible Markov Chains</a> 
               [From Qian Jiang (jiang1h(AT)uwindsor.ca), Jun 08 2009]
%F A002807 E.g.f.: (-1/4)*exp(x)*(2*ln(1-x)+2*x+x^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Oct 26 2004
%F A002807 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
%Y A002807 Cf. A117130, A099198, A099201, A070968.
%Y A002807 Sequence in context: A085640 A069378 A117130 this_sequence A124610 A002683 
               A126475
%Y A002807 Adjacent sequences: A002804 A002805 A002806 this_sequence A002808 A002809 
               A002810
%K A002807 nonn,easy,nice
%O A002807 0,5
%A A002807 N. J. A. Sloane (njas(AT)research.att.com).

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