

A040175


a(n) = n! times probability that an ordered pair of elements of S_n chosen at random (with replacement) generate S_n.


5



3, 9, 57, 318, 3090, 24666, 234879, 2381481, 26777922, 324421053, 4265966685
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OFFSET

3,1


COMMENTS

Probability is A040173(n)/A040174(n) = a(n)/n!.
Note that a(2)=3/2 is not integer.


REFERENCES

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), 621630.


LINKS

Table of n, a(n) for n=3..13.
L. Babai, The probability of generating the symmetric group, J. Combin. Theory, A52 (1989), 148153.
J. D. Dixon, The probability of generating the symmetric group, Math. Z. 110 (1969) 199205.
T. Luczak and L. Pyber, On random generation of the symmetric group, Combin. Probab. Comput., 2 (1993), 505512.
A. Maroti and C. M. Tamburini, Bounds for the probability of generating the symmetric and alternating groups, Arch. Math. (Basel), 96 (2011), 115121.


FORMULA

a(n) = A071605(n)/n!.


EXAMPLE

Probabilities for n=1,2,3,... are 1, 3/4, 1/2, 3/8, 19/40, ...


CROSSREFS

Cf. A071605, A135474.
Sequence in context: A128681 A292333 A294785 * A192252 A105466 A261244
Adjacent sequences: A040172 A040173 A040174 * A040176 A040177 A040178


KEYWORD

nonn,more,nice


AUTHOR

Dan Hoey


EXTENSIONS

Edited by Max Alekseyev, Jan 28 2012
a(10)a(13) from Stephen A. Silver, Feb 21 2013


STATUS

approved



