Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 Nov 28 2019 07:16:32
%S 1,1,1,9,22,77,400,2624,20747,183544,1826374,20045348,240262047,
%T 3120641718,43665293393,654731266933,10472819759734,178001257647196,
%U 3203520381407270,60859480965537820,1217072840308660049
%N Number of orbits of the direct square of the alternating group A_n^2 where A_n acts by conjugation.
%H Derek Lim, <a href="/A327150/b327150.txt">Table of n, a(n) for n = 0..61</a>
%H MathOverflow, <a href="http://mathoverflow.net/questions/41337/a-general-formula-for-the-number-of-conjugacy-classes-of-mathbbs-n-times-m/">A general formula for the number of conjugacy classes of S_n×S_n acted on by S_n</a>
%F a(n) = (n!/2) * Sum_{K conjugacy class in A_n} 1/|K|.
%e 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.
%o (GAP) G:= AlternatingGroup(n);; Size(G)*Sum(List(ConjugacyClasses(G), K -> 1/Size(K)));
%Y Cf. A000702, A110143, A327014, A327151.
%K nonn
%O 0,4
%A _Derek Lim_, Aug 23 2019