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A086373
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Number of ordered triples (a,b,c) of elements of the symmetric group S_n such that a,b,c generate S_n.
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1
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1, 7, 168, 10080, 1401120, 303730560, 109469465280, 56335746378240, 41263790481123840, 41372254858231987200, 55175243131277553715200, 95478523289749232323891200, 209996618265179127555767193600
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OFFSET
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1,2
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LINKS
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PROG
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(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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003
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EXTENSIONS
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STATUS
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approved
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