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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
1, 7, 168, 10080, 1401120, 303730560, 109469465280, 56335746378240, 41263790481123840, 41372254858231987200, 55175243131277553715200, 95478523289749232323891200, 209996618265179127555767193600
OFFSET
1,2
PROG
(GAP)
a := function(n)
local tom, mu, lens, orders, num, k;
tom := TableOfMarks(Concatenation("S", String(n)));
if tom = fail then tom := TableOfMarks(SymmetricGroup(n)); fi;
mu := MoebiusTom(tom).mu;
lens := LengthsTom(tom);
orders := OrdersTom(tom);
num := 0;
for k in [1 .. Length(lens)] do
if IsBound(mu[k]) then
num := num + mu[k] * lens[k] * orders[k]^3;
fi;
od;
return num;
end; # Stephen A. Silver, Feb 20 2013
CROSSREFS
Sequence in context: A220991 A165388 A124126 * A162131 A258299 A012067
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003
EXTENSIONS
1 more term from David Wasserman, Mar 10 2005
a(6)-a(13) from Stephen A. Silver, Feb 20 2013
STATUS
approved