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A086373 Number of ordered triples (a,b,c) of elements of the symmetric group S_n such that a,b,c generate S_n.

%I A086373 #9 Feb 21 2013 07:07:06
%S A086373 1,7,168,10080,1401120,303730560,109469465280,56335746378240,
%T A086373 41263790481123840,41372254858231987200,55175243131277553715200,
%U A086373 95478523289749232323891200,209996618265179127555767193600
%N A086373 Number of ordered triples (a,b,c) of elements of the symmetric group S_n such that a,b,c generate S_n.
%o A086373 (GAP)
%o A086373 a := function(n)
%o A086373   local tom, mu, lens, orders, num, k;
%o A086373   tom := TableOfMarks(Concatenation("S",String(n)));
%o A086373   if tom = fail then tom := TableOfMarks(SymmetricGroup(n)); fi;
%o A086373   mu :=  MoebiusTom(tom).mu;
%o A086373   lens := LengthsTom(tom);
%o A086373   orders := OrdersTom(tom);
%o A086373   num := 0;
%o A086373   for k in [1 .. Length(lens)] do
%o A086373     if IsBound(mu[k]) then
%o A086373       num := num + mu[k] * lens[k] * orders[k]^3;
%o A086373     fi;
%o A086373   od;
%o A086373   return num;
%o A086373 end; # _Stephen A. Silver_, Feb 20 2013
%Y A086373 Cf. A071605, A001691.
%K A086373 nonn
%O A086373 1,2
%A A086373 Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003
%E A086373 1 more term from _David Wasserman_, Mar 10 2005
%E A086373 a(6)-a(13) from _Stephen A. Silver_, Feb 20 2013