A060348 -id:A060348 - cp's OEIS frontend

A060349 a(n) = n^(n+2)(n^2 - 1)(n+3)(n+2)(5*n - 7)/5760.

81, 5824, 328125, 16901136, 847425747, 42630905856, 2186213819427, 115293750000000, 6283133610195442, 354769407810994176, 20781472563720847342, 1263485180096661430272, 79727340621643066406250, 5219469342167970210643968, 354305349685394263423480746

Offset: 3

Noam Katz (noamkj(AT)hotmail.com), Mar 30 2001

nonn

For n >= 3, a(n) is the number of nonequivalent primitive meromorphic functions with one pole of order n on a Riemann surface of genus 2.

B. Shapiro, M. Shapiro and A. Vainshtein, Ramified coverings of S^2 with one degenerate branching point and enumeration of edge-ordered graphs, Amer. Math. Soc. Transl., Vol. 180 (1997), pp. 219-227.

Harry J. Smith, Table of n, a(n) for n = 3..200

Cf. A007830, A060348.

Table[(n^(n+2) (n^2-1)(n+3)(n+2)(5n-7))/5760,{n,3,20}] (* Harvey P. Dale, Jan 10 2013 *)

{ for (n=3, 200, write("b060349.txt", n, " ", n^(n + 2)*(n^2 - 1)*(n + 3)*(n + 2)*(5*n - 7)/5760); ) } \\ Harry J. Smith, Jul 04 2009

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

Original entry on oeis.org

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

Offset: 1

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

nonn

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.

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

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).

Cf. A060348, A000272.

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

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

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

More terms from James Sellers, Apr 13 2001

cp's OEIS Frontend

A060349 a(n) = n^(n+2)(n^2 - 1)(n+3)(n+2)(5*n - 7)/5760.

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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.

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cp's OEIS Frontend

A060349 a(n) = n^(n+2)*(n^2 - 1)*(n+3)*(n+2)*(5*n - 7)/5760.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI

Formula

Extensions

A060349 a(n) = n^(n+2)(n^2 - 1)(n+3)(n+2)(5*n - 7)/5760.