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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
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OFFSET
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1,3
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COMMENTS
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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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LINKS
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FORMULA
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a(n) = (1/24) * (n^2 - 1) * n^(n + 1).
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EXAMPLE
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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
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for n from 1 to 30 do printf(`%d, `, 1/24 * (n^2 - 1) * n^(n + 1)) od:
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 13 2001
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EXTENSIONS
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STATUS
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approved
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