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A087132 a(n) is the sum of the squares of the sizes of the conjugacy classes in the symmetric group S_n. 4
1, 2, 14, 146, 2602, 71412, 2675724, 134269158, 8747088662, 717107850956, 72007758701716, 8736187050160132, 1258160557017484564, 212232765513231245096, 41518913481377118146520, 9309797624034705006898470, 2374942651509463493006400390, 683620331016710787068868581580 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is a natural quantity to consider when viewing the symmetric group (Sym_n) as a set. a(n) is the sum over all elements of Sym_n of the size of their conjugacy class. Each conjugacy class is thus counted as many times as its size, giving a sum of squares. - Olivier Gérard, Feb 12 2012

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..57

Simon R. Blackburn, John R. Britnell, Mark Wildon, The probability that a pair of elements of a finite group are conjugate, arXiv:1108.1784, 2011

Philippe Flajolet, Éric Fusy, Xavier Gourdon, Daniel Panario and Nicolas Pouyanne, A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics, arXiv:math.CO/0606370

FORMULA

a(n) = (n!)^2 * (c/n^2 + O((log n)/n^3)), where c = prod_{k>=1}sum_{n>=0}1/(k*n!)^2 ~ 4.263403514152669778298935... (see A246879). [Corrected by Vaclav Kotesovec, Sep 21 2014]

PROG

(MAGMA) [ &+[ c[2]^2 : c in ClassesData(Sym(n))] : n in [1..10]]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

CROSSREFS

Cf. A000041, A073906, A192983, A206820. - Olivier Gérard, Feb 12 2012

Cf. A246879.

Sequence in context: A245267 A271564 A100510 * A036079 A121227 A250916

Adjacent sequences:  A087129 A087130 A087131 * A087133 A087134 A087135

KEYWORD

nonn

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 18 2003

EXTENSIONS

More terms from Vladeta Jovovic, Oct 22 2003

More terms from Vaclav Kotesovec, Sep 21 2014

STATUS

approved

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Last modified February 20 00:51 EST 2018. Contains 299357 sequences. (Running on oeis4.)