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A007060
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Number of ways n couples can sit in a row without any spouses next to each other.
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6
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1, 0, 8, 240, 13824, 1263360, 168422400, 30865121280, 7445355724800, 2287168006717440, 871804170613555200, 403779880746418176000, 223346806774106790297600, 145427383048755178635264000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) approaches (2n)!*exp(-1) as n goes to infinity.
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LINKS
| Eric Weisstein's World of Mathematics, Cocktail Party Graph
Eric Weisstein's World of Mathematics, Hamiltonian Path
Andrew Woods, Table of n, a(n) for n = 0..100
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FORMULA
| a(n) = (Pi*BesselI(n+1/2,1)*(-1)^n+BesselK(n+1/2,1))*exp(-1)*(2/Pi)^(1/2)*2^n*n! [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 12 2009]
a(n) = (-1)^n*2^n*n!*A000806(n), n>0. [From Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 19 2009]
a(n) = n!*hypergeom([ -n, n+1],[],1/2)*(-2)^n [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 13 2009]
a(n) = 2^n * A114938(n) [From Toby Gottfried, Nov 22, 2010]
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EXAMPLE
| For n = 2, the a(2) = 8 solutions for the couples {1,2} and {3,4} are {1324, 1423, 2314, 2413, 3142, 3241, 4132, 4231}.
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MAPLE
| sum((-1)^i*binomial(n, i)*(2^i*abs((2*n-i))!), i=0..n);
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MATHEMATICA
| Table[Sum(-1)^i Binomial[n, i] (2n-i)! 2^i, {i, 0, n}], {n, 0, 20}]
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CROSSREFS
| Sequence in context: A134504 A145418 A067360 * A158263 A115613 A085524
Adjacent sequences: A007057 A007058 A007059 * A007061 A007062 A007063
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KEYWORD
| nonn,easy,nice
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AUTHOR
| David.Roberts.Keeney(AT)directory.Reed.EDU (David Roberts Keeney)
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EXTENSIONS
| More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 11 2001
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