

A001691


Number of twoelement generating sets in the symmetric group S_n.
(Formerly M4660 N1995)


3



0, 1, 9, 108, 3420, 114480, 7786800, 497266560, 42616445760, 4320959126400, 534444478444800, 77699101730342400, 13282131639801024000
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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), 108116.


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



