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A278705
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Number of length-4 cycles in all simple labeled graphs on n nodes.
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1
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12, 960, 92160, 13762560, 3523215360, 1623497637888, 1385384650997760, 2229281815548395520, 6848353737364671037440, 40517904423021555933511680, 464691742246749620690258755584, 10382058415869198798257999252029440, 453599053561602541628424159320667586560
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OFFSET
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4,1
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LINKS
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FORMULA
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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).
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MATHEMATICA
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Table[FactorialPower[n, 4]/(8) 2^(Binomial[n, 2] - 4), {n, 0, 15}]
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PROG
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(Magma) [n*(n-1)*(n-2)*(n-3)/8*2^(Binomial(n, 2)-4): n in [4..20]]; // _Vincenzo Lubrandi_, Nov 27 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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