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A060603
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Number of ways of expressing an n-cycle in the symmetric group S_n as a product of n+1 transpositions.
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1
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0, 1, 27, 640, 15625, 408240, 11529602, 352321536, 11622614670, 412500000000, 15692141883605, 637501182050304, 27561634699895023, 1263990776407224320, 61305144653320312500, 3135946492530623774720, 168757013424812699892108
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| For n >= 3 a(n) = A060348(n) * n. The number of ways of expressing an n-cycle in the symmetric group S_n as a product of n-1 transpositions was given in the comment to A000272.
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REFERENCES
| D. M. Jackson - Some Combinatorial Problems Associated with Products of Conjugacy Classes of the Symmetric Group, Journal of combinatorial theory Seies A, 49 363-369(1988).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,200
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FORMULA
| a(n) = 1/24 * (n^2 - 1) * n^(n + 1)
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EXAMPLE
| a(2) = 1 because in S_2 the only way to write (12) as a product of 3 transpositions is: (12) = (12)(12)(12)
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MAPLE
| for n from 1 to 30 do printf(`%d, `, 1/24 * (n^2 - 1) * n^(n + 1)) od:
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PROG
| (PARI) { for (n=1, 200, write("b060603.txt", n, " ", (n^2 - 1) * n^(n + 1)/24); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 07 2009]
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CROSSREFS
| A060348, A000272.
Sequence in context: A185883 A099753 A046359 * A116988 A113364 A095898
Adjacent sequences: A060600 A060601 A060602 * A060604 A060605 A060606
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KEYWORD
| nonn
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AUTHOR
| Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 13 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 13 2001
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