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

Author

Derek Lim, Aug 23 2019

Keywords

• nonn

Examples

			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.
		

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

Crossrefs

Cf. A000702, A110143, A327014, A327151.

Programs

GAP

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

Formula

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