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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


%S 1,2,14,146,2602,71412,2675724,134269158,8747088662,717107850956,

%T 72007758701716,8736187050160132,1258160557017484564,

%U 212232765513231245096,41518913481377118146520,9309797624034705006898470,2374942651509463493006400390,683620331016710787068868581580

%N a(n) is the sum of the squares of the sizes of the conjugacy classes in the symmetric group S_n.

%C 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

%H Vaclav Kotesovec, <a href="/A087132/b087132.txt">Table of n, a(n) for n = 1..57</a>

%H Simon R. Blackburn, John R. Britnell, Mark Wildon, <a href="http://arxiv.org/abs/1108.1784">The probability that a pair of elements of a finite group are conjugate</a>, arXiv:1108.1784, 2011

%H Philippe Flajolet, Éric Fusy, Xavier Gourdon, Daniel Panario and Nicolas Pouyanne, <a href="http://arXiv.org/abs/math.CO/0606370">A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics</a>, arXiv:math.CO/0606370

%F 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]

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

%Y Cf. A000041, A073906, A192983, A206820. - _Olivier Gérard_, Feb 12 2012

%Y Cf. A246879.

%K nonn

%O 1,2

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

%E More terms from _Vladeta Jovovic_, Oct 22 2003

%E More terms from _Vaclav Kotesovec_, Sep 21 2014

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Last modified February 22 01:52 EST 2019. Contains 320381 sequences. (Running on oeis4.)