A327150 Number of orbits of the direct square of the alternating group A_n^2 where A_n acts by conjugation.

1, 1, 1, 9, 22, 77, 400, 2624, 20747, 183544, 1826374, 20045348, 240262047, 3120641718, 43665293393, 654731266933, 10472819759734, 178001257647196, 3203520381407270, 60859480965537820, 1217072840308660049

Offset

0,4

Links

Derek Lim, Table of n, a(n) for n = 0..61

MathOverflow, A general formula for the number of conjugacy classes of S_n×S_n acted on by S_n

Formula

a(n) = (n!/2) * Sum_{K conjugacy class in A_n} 1/|K|.

Example

For n = 3, representatives of the n=9 orbits are (e,e), (e,(123)), (e,(132)), ((123),e), ((132),e), ((123),(123)), ((123),(132)), ((132),(123)), ((132),(132)), where e is the identity.

Prog

(GAP) G:= AlternatingGroup(n);; Size(G)*Sum(List(ConjugacyClasses(G), K -> 1/Size(K)));

Crossrefs

Cf. A000702, A110143, A327014, A327151.

Sequence in context: A197498 A287497 A232024 * A264651 A113519 A300462

Adjacent sequences: A327147 A327148 A327149 * A327151 A327152 A327153

Keyword

nonn

Author

Derek Lim, Aug 23 2019

Status

approved