A060603 Number of ways of expressing an n-cycle in the symmetric group S_n as a product of n+1 transpositions.

0, 1, 27, 640, 15625, 408240, 11529602, 352321536, 11622614670, 412500000000, 15692141883605, 637501182050304, 27561634699895023, 1263990776407224320, 61305144653320312500, 3135946492530623774720, 168757013424812699892108

Offset: 1

Author

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

Keywords

• nonn

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.

Examples

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

Links

• Harry J. Smith, Table of n, a(n) for n = 1..200
• 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).

Crossrefs

Cf. A060348, A000272.

Programs

Maple

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

PARI

a(n)={(n^2 - 1) * n^(n + 1)/24} \\ Harry J. Smith, Jul 07 2009

Formula

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

Extensions

More terms from James Sellers, Apr 13 2001