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A159662
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Any number of necklaces made from n distinct colored beads then linearly arranged in a display case.
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0
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1, 1, 3, 13, 77, 572, 5114, 53406, 637818, 8572434, 128041458, 2103949314, 37716766350, 732505270152, 15320768312784, 343335554738328, 8207083694470392, 208444177385240472, 5605513502234263272
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is the number of ways to seat n people at circular tables then linearly order the tables. Two seating arrangements are considered identical if each person has the same two neighbors in both.
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FORMULA
| E.g.f.:1/(1-x/2-x^2/4+Log[1-x]/2)
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EXAMPLE
| a(3)=13 because There are 3! ways to arrange the three necklaces consisting of a single bead. There are 2! ways to arrange each of the 3 collections of necklaces of length two and one. There is 1 way to display the unique necklace having three beads. 3!+2!*3+1=13
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MATHEMATICA
| CoefficientList[Series[1/(1 - x/2 - x^2/4 + Log[1 - x]/2), {x, 0, 20}], x]* Table[n!, {n, 0, 20}]
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CROSSREFS
| Cf. A001710
Sequence in context: A059040 A189239 A074530 * A032035 A127127 A043301
Adjacent sequences: A159659 A159660 A159661 * A159663 A159664 A159665
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KEYWORD
| nonn
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AUTHOR
| Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 19 2009
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