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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. 1

%I

%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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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)