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 A001691 Number of two-element 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 15 06:58 EDT 2024. Contains 374324 sequences. (Running on oeis4.)