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%I #9 Feb 21 2013 07:07:06
%S 1,7,168,10080,1401120,303730560,109469465280,56335746378240,
%T 41263790481123840,41372254858231987200,55175243131277553715200,
%U 95478523289749232323891200,209996618265179127555767193600
%N Number of ordered triples (a,b,c) of elements of the symmetric group S_n such that a,b,c generate S_n.
%o (GAP)
%o a := function(n)
%o local tom, mu, lens, orders, num, k;
%o tom := TableOfMarks(Concatenation("S",String(n)));
%o if tom = fail then tom := TableOfMarks(SymmetricGroup(n)); fi;
%o mu := MoebiusTom(tom).mu;
%o lens := LengthsTom(tom);
%o orders := OrdersTom(tom);
%o num := 0;
%o for k in [1 .. Length(lens)] do
%o if IsBound(mu[k]) then
%o num := num + mu[k] * lens[k] * orders[k]^3;
%o fi;
%o od;
%o return num;
%o end; # _Stephen A. Silver_, Feb 20 2013
%Y Cf. A071605, A001691.
%K nonn
%O 1,2
%A Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003
%E 1 more term from _David Wasserman_, Mar 10 2005
%E a(6)-a(13) from _Stephen A. Silver_, Feb 20 2013
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