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%I #15 Sep 08 2022 08:46:18
%S 12,960,92160,13762560,3523215360,1623497637888,1385384650997760,
%T 2229281815548395520,6848353737364671037440,
%U 40517904423021555933511680,464691742246749620690258755584,10382058415869198798257999252029440,453599053561602541628424159320667586560
%N Number of length-4 cycles in all simple labeled graphs on n nodes.
%H Peter Maceli, <a href="http://www.columbia.edu/~plm2109/nine.pdf">Class Nine: Random Graphs</a>
%F a(n) = binomial(n,4)*(4!/8)*2^binomial(n,2). The number of length k cycles in all simple labeled graphs on n nodes is binomial(n,k)*(k!/(2*k))*2^binomial(n,2).
%t Table[FactorialPower[n, 4]/(8) 2^(Binomial[n, 2] - 4), {n, 0, 15}]
%o (Magma) [n*(n-1)*(n-2)*(n-3)/8*2^(Binomial(n, 2)-4): n in [4..20]]; // _Vincenzo Lubrandi_, Nov 27 2016
%K nonn
%O 4,1
%A _Geoffrey Critzer_, Nov 26 2016
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