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A070733 Size of largest conjugacy class in A_n, the alternating group on n symbols.

%I A070733 #17 Jul 12 2025 08:34:36
%S A070733 1,1,1,4,20,90,630,3360,30240,226800,2494800,23950080,311351040,
%T A070733 3632428800,54486432000,747242496000,12703122432000,200074178304000,
%U A070733 3801409387776000,67580611338240000,1419192838103040000,28100018194440192000,646300418472124416000
%N A070733 Size of largest conjugacy class in A_n, the alternating group on n symbols.
%C A070733 For n > 5, the largest conjugacy class in A_n corresponds to the cycle type (n-2, 2) if n is even, (n-3, 2, 1) if n is odd. - _Eric M. Schmidt_, Sep 13 2014
%H A070733 Eric M. Schmidt, <a href="/A070733/b070733.txt">Table of n, a(n) for n = 1..100</a>
%F A070733 For n > 5, a(n) = n!/(2(n-2)) if n is even, a(n) = n!/(2(n-3)) if n is odd. - _Eric M. Schmidt_, Sep 13 2014
%F A070733 Sum_{n>=1} 1/a(n) = 111/10 + 1/e - 3*e. - _Amiram Eldar_, Jul 12 2025
%t A070733 a[n_] := (n!/2) / If[OddQ[n],  n-3, n-2]; a[1] = a[2] = a[3] = 1; a[4] = 4; a[5] = 20; Array[a, 20] (* _Amiram Eldar_, Jul 12 2025 *)
%o A070733 (GAP)
%o A070733 a:=function(n)
%o A070733 local G,CC,SCC,SCC1;
%o A070733 G:=AlternatingGroup(n);
%o A070733 CC:=ConjugacyClasses(G);;
%o A070733 SCC:=List(CC,Size);
%o A070733 return Maximum(SCC);
%o A070733 end;;  #  _W. Edwin Clark_, Feb 02 2014
%o A070733 (PARI) a(n) = if(n < 6, [1, 1, 1, 4, 20][n], (n!/2) / if(n % 2,  n-3, n-2)); \\ _Amiram Eldar_, Jul 12 2025
%Y A070733 Cf. A059171, A001710, A000702, A029726.
%K A070733 nonn
%O A070733 1,4
%A A070733 Sharon Sela (sharonsela(AT)hotmail.com), May 14 2002
%E A070733 More terms from _Eric M. Schmidt_, Sep 13 2014