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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..13.

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

Cf. A071605, A001691.

Sequence in context: A220991 A165388 A124126 * A162131 A258299 A012067

Adjacent sequences:  A086370 A086371 A086372 * A086374 A086375 A086376

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

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)