A001691 Number of two-element generating sets in the symmetric group S_n. (Formerly M4660 N1995)

0, 1, 9, 108, 3420, 114480, 7786800, 497266560, 42616445760, 4320959126400, 534444478444800, 77699101730342400, 13282131639801024000

Offset

1,3

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

J. Denes, Some combinatorial properties of transformations and their connections with the theory of graphs, J. Combin. Theory, 9 (1970), 108-116.

Formula

a(n) = A071605(n)/2 for n > 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] * Binomial(orders[k], 2);
    fi;
  od;
  return num;
end; # Stephen A. Silver, Feb 20 2013

Crossrefs

Cf. A071605, A086373.

Sequence in context: A166907 A051606 A330876 * A157906 A166846 A058421

Adjacent sequences: A001688 A001689 A001690 * A001692 A001693 A001694

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(8)-a(9) (derived from A071605) added by Stephen A. Silver, Feb 17 2013

a(10)-a(13) added by Stephen A. Silver, Feb 20 2013

Status

approved