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A060603
Number of ways of expressing an n-cycle in the symmetric group S_n as a product of n+1 transpositions.
1
0, 1, 27, 640, 15625, 408240, 11529602, 352321536, 11622614670, 412500000000, 15692141883605, 637501182050304, 27561634699895023, 1263990776407224320, 61305144653320312500, 3135946492530623774720, 168757013424812699892108
OFFSET
1,3
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.
LINKS
D. M. Jackson, Some Combinatorial Problems Associated with Products of Conjugacy Classes of the Symmetric Group, Journal of Combinatorial Theory, Series A, 49 363-369(1988).
FORMULA
a(n) = (1/24) * (n^2 - 1) * n^(n + 1).
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).
MAPLE
for n from 1 to 30 do printf(`%d, `, 1/24 * (n^2 - 1) * n^(n + 1)) od:
PROG
(PARI) a(n)={(n^2 - 1) * n^(n + 1)/24} \\ Harry J. Smith, Jul 07 2009
CROSSREFS
Sequence in context: A231292 A046359 A223500 * A116988 A113364 A095898
KEYWORD
nonn
AUTHOR
Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 13 2001
EXTENSIONS
More terms from James A. Sellers, Apr 13 2001
STATUS
approved