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%I M4660 N1995 #35 Feb 01 2022 07:12:34
%S 0,1,9,108,3420,114480,7786800,497266560,42616445760,4320959126400,
%T 534444478444800,77699101730342400,13282131639801024000
%N Number of two-element generating sets in the symmetric group S_n.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. Denes, <a href="http://dx.doi.org/10.1016/S0021-9800(70)80017-5">Some combinatorial properties of transformations and their connections with the theory of graphs</a>, J. Combin. Theory, 9 (1970), 108-116.
%F a(n) = A071605(n)/2 for n > 2.
%o (GAP)
%o a := function(n)
%o local tom, mu, lens, orders, num, k;
%o tom := TableOfMarks(Concatenation("S",String(n)));
%o if tom = fail then tom := TableOfMarks(SymmetricGroup(n)); fi;
%o mu := MoebiusTom(tom).mu;
%o lens := LengthsTom(tom);
%o orders := OrdersTom(tom);
%o num := 0;
%o for k in [1 .. Length(lens)] do
%o if IsBound(mu[k]) then
%o num := num + mu[k] * lens[k] * Binomial(orders[k],2);
%o fi;
%o od;
%o return num;
%o end; # _Stephen A. Silver_, Feb 20 2013
%Y Cf. A071605, A086373.
%K nonn,more
%O 1,3
%A _N. J. A. Sloane_
%E a(8)-a(9) (derived from A071605) added by _Stephen A. Silver_, Feb 17 2013
%E a(10)-a(13) added by _Stephen A. Silver_, Feb 20 2013
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