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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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%I #16 Jul 03 2018 02:37:14

%S 0,1,27,640,15625,408240,11529602,352321536,11622614670,412500000000,

%T 15692141883605,637501182050304,27561634699895023,1263990776407224320,

%U 61305144653320312500,3135946492530623774720,168757013424812699892108

%N Number of ways of expressing an n-cycle in the symmetric group S_n as a product of n+1 transpositions.

%C 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.

%H Harry J. Smith, <a href="/A060603/b060603.txt">Table of n, a(n) for n = 1..200</a>

%H D. M. Jackson, <a href="http://dx.doi.org/10.1016/0097-3165(88)90062-3">Some Combinatorial Problems Associated with Products of Conjugacy Classes of the Symmetric Group</a>, Journal of Combinatorial Theory, Series A, 49 363-369(1988).

%F a(n) = (1/24) * (n^2 - 1) * n^(n + 1).

%e a(2) = 1 because in S_2 the only way to write (12) as a product of 3 transpositions is (12) = (12)(12)(12).

%p for n from 1 to 30 do printf(`%d,`,1/24 * (n^2 - 1) * n^(n + 1)) od:

%o (PARI) a(n)={(n^2 - 1) * n^(n + 1)/24} \\ _Harry J. Smith_, Jul 07 2009

%Y Cf. A060348, A000272.

%K nonn

%O 1,3

%A Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 13 2001

%E More terms from _James A. Sellers_, Apr 13 2001