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Number of conjugacy classes in the symmetric group S_n with distinct cardinality.
9

%I #22 Dec 24 2024 08:19:57

%S 1,1,3,4,6,7,11,16,23,30,40,58,69,95,119,151,184,240,297,361,452,554,

%T 663,817,980,1177,1402,1665,1995,2346,2774,3259,3837,4466,5222,6057,

%U 7061,8159,9450,10917,12533,14408,16570,18958,21623,24681,28123,32000,36232

%N Number of conjugacy classes in the symmetric group S_n with distinct cardinality.

%C a(n) is the number of distinct entries of row n in the triangle of refined rencontres numbers A181897. - _Tilman Piesk_, Apr 01 2012

%H Sean A. Irvine, <a href="/A073906/b073906.txt">Table of n, a(n) for n = 1..120</a> (terms 1..60 from Alois P. Heinz)

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%t Map[Length,Map[Union,Table[f[list_]:=Total[list]!/Apply[Times,list]/Apply[Times,Table[Count[list,n]!,{n,1,m}]];Map[f,Partitions[m]],{m,1,30}]]] (* _Geoffrey Critzer_, Mar 25 2013 *)

%Y Cf. A000041, A181897.

%K nonn

%O 1,3

%A _Vladeta Jovovic_, Sep 03 2002

%E a(41)-a(49) from _Alois P. Heinz_, Feb 04 2014