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A242099 Number of conjugacy classes of the symmetric group S_n when conjugating by the dihedral group D_n.

%I A242099 #22 Aug 25 2014 04:41:51
%S A242099 1,2,3,8,18,84,387,2670,20373,182796,1816325,19973962,239523846,
%T A242099 3113717784,43589470208,653840410004,10461400104968,177843770847822,
%U A242099 3201186945761289,60822551319191028,1216451005946790780,25545471110008012860,562000363929678643211
%N A242099 Number of conjugacy classes of the symmetric group S_n when conjugating by the dihedral group D_n.
%H A242099 Eric M. Schmidt, <a href="/A242099/b242099.txt">Table of n, a(n) for n = 1..100</a>
%F A242099 a(n) = (A061417(n) + b(n))/2, where b(n) = ((n-1)/2)! * 2^((n-1)/2) if n is odd, b(n) = ((n/2)! + (n/2-1)!) * 2^(n/2-1) if n is even. - _Eric M. Schmidt_, Aug 23 2014
%o A242099 (GAP) List([1..11],n->Size(OrbitsDomain(DihedralGroup(IsPermGroup,2*n),SymmetricGroup(IsPermGroup,n),\^)));
%o A242099 (Sage) def a(n) : return (sum(euler_phi(n//d) * (n//d)^d * factorial(d) for d in divisors(n))//n + [(factorial(n//2) + factorial((n+1)//2 - 1)) * 2^(n//2-1), factorial((n-1)//2) * 2^((n-1)//2)][n%2]) // 2 # _Eric M. Schmidt_, Aug 23 2014
%Y A242099 Cf. A242101 (by alternating group), A000041 (by symmetric group itself), A061417 (by cyclic group).
%K A242099 nonn
%O A242099 1,2
%A A242099 _Attila Egri-Nagy_, Aug 14 2014
%E A242099 More terms from _Eric M. Schmidt_, Aug 23 2014