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

1, 2, 3, 8, 18, 84, 387, 2670, 20373, 182796, 1816325, 19973962, 239523846, 3113717784, 43589470208, 653840410004, 10461400104968, 177843770847822, 3201186945761289, 60822551319191028, 1216451005946790780, 25545471110008012860, 562000363929678643211

Offset

1,2

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..100

Formula

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

Prog

(GAP) List([1..11], n->Size(OrbitsDomain(DihedralGroup(IsPermGroup, 2*n), SymmetricGroup(IsPermGroup, n), \^)));
(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

Crossrefs

Cf. A242101 (by alternating group), A000041 (by symmetric group itself), A061417 (by cyclic group).

Sequence in context: A157015 A240645 A273754 * A041205 A002356 A166302

Adjacent sequences: A242096 A242097 A242098 * A242100 A242101 A242102

Keyword

nonn

Author

Attila Egri-Nagy, Aug 14 2014

Extensions

More terms from Eric M. Schmidt, Aug 23 2014

Status

approved