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A167406
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Sequence a(n) gives the number of ways to seat 2n people around a circular table so that person i does not sit across from person n+i for any 1 <= i <= n.
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0
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0, 4, 64, 2880, 208896, 23193600, 3640688640, 768126320640, 209688566169600, 71921062285148160, 30278182590480384000, 15350836256712740044800, 9225766813653105691852800, 6485670333458406942179328000, 5272823572160895949091320627200
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (n!)^2/(2*n)*sum{k = 0..n+1}((-1)^k/k!*binomial(2*n-2*k, n-k)*2^k).
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EXAMPLE
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When n=2, there are four people seated around a circular table. Person 1 can sit across from either person 2 or person 4, and person 3 can sit either to the left or to the right of person 1. Thus a(2) = 2*2=4.
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PROG
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(PARI) a(n) = n!^2/(2*n)*sum(k = 0, n+1, (-1)^k/k!*binomial(2*n-2*k, n-k)*2^k) \\ Michel Marcus, Jul 11 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Steven Klee (klees(AT)math.washington.edu), Nov 03 2009
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EXTENSIONS
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STATUS
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approved
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