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%I #29 Dec 25 2023 10:02:34
%S 1,1,1,2,5,9,22,37,112,195,423,780,2401,4409
%N Number of conjugacy classes of subgroups of the symmetric which are also subgroups of the alternating group.
%H GAP, <a href="https://www.gap-system.org/Packages/tomlib.html">GAP package TomLib, The GAP Library of Tables of Marks</a>.
%H Liam Naughton, <a href="http://www.maths.nuigalway.ie/~liam/CountingSubgroups.g">CountingSubgroups.g</a>
%H Liam Naughton and Goetz Pfeiffer, <a href="http://arxiv.org/abs/1211.1911">Integer sequences realized by the subgroup pattern of the symmetric group</a>, arXiv:1211.1911 [math.GR], 2012-2013.
%H Liam Naughton and Goetz Pfeiffer, <a href="https://web.archive.org/web/20210307075628/http://schmidt.nuigalway.ie/tomlib/">Tomlib, The GAP table of marks library</a>.
%o (GAP)
%o # GAP 4.11.1
%o n := 9;;
%o GS := List( [1..n], m-> SymmetricGroup(m));;
%o subS := List( GS, x-> ConjugacyClassesSubgroups(x));;
%o repS := List( subS, x-> List(x, Representative));;
%o GA := List( [1..n], m-> AlternatingGroup(m));;
%o List( [1..n], m-> Number( repS[m], x-> IsSubgroup( GA[m], x)));
%o # _Peter Dolland_, Jul 15 2021
%K nonn,more
%O 0,4
%A _Liam Naughton_, Nov 23 2012
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