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%I #23 Sep 11 2015 05:50:28
%S 3,9,57,318,3090,24666,234879,2381481,26777922,324421053,4265966685
%N a(n) = n! times probability that an ordered pair of elements of S_n chosen at random (with replacement) generate S_n.
%C Probability is A040173(n)/A040174(n) = a(n)/n!.
%C Note that a(2)=3/2 is not integer.
%D J. D. Dixon, Problem 923 (BCC20.17), Indecomposable permutations and transitive groups, in Research Problems from the 20th British Combinatorial Conference, Discrete Math., 308 (2008), 621-630.
%H L. Babai, <a href="http://dx.doi.org/10.1016/0097-3165(89)90068-X">The probability of generating the symmetric group</a>, J. Combin. Theory, A52 (1989), 148-153.
%H J. D. Dixon, <a href="http://dx.doi.org/10.1007/BF01110210">The probability of generating the symmetric group</a>, Math. Z. 110 (1969) 199-205.
%H T. Luczak and L. Pyber, <a href="http://dx.doi.org/10.1017/S0963548300000869">On random generation of the symmetric group</a>, Combin. Probab. Comput., 2 (1993), 505-512.
%H A. Maroti and C. M. Tamburini, <a href="http://dx.doi.org/10.1007/s00013-010-0216-z">Bounds for the probability of generating the symmetric and alternating groups</a>, Arch. Math. (Basel), 96 (2011), 115-121.
%F a(n) = A071605(n)/n!.
%e Probabilities for n=1,2,3,... are 1, 3/4, 1/2, 3/8, 19/40, ...
%Y Cf. A071605, A135474.
%K nonn,more,nice
%O 3,1
%A _Dan Hoey_
%E Edited by _Max Alekseyev_, Jan 28 2012
%E a(10)-a(13) from _Stephen A. Silver_, Feb 21 2013
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