The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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: A271564 A100510 A333592 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)