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, 7, 168, 10080, 1401120, 303730560, 109469465280, 56335746378240, 41263790481123840, 41372254858231987200, 55175243131277553715200, 95478523289749232323891200, 209996618265179127555767193600

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003

Keywords

• nonn

Crossrefs

Cf. A071605, A001691.

Programs

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

Extensions

1 more term from David Wasserman, Mar 10 2005

a(6)-a(13) from Stephen A. Silver, Feb 20 2013