A040175 - OEIS

A040175

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

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

(list; graph; refs; listen; history; text; internal format)

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), 621-630.

LINKS

Table of n, a(n) for n=3..13.

L. Babai, The probability of generating the symmetric group, J. Combin. Theory, A52 (1989), 148-153.

J. D. Dixon, The probability of generating the symmetric group, Math. Z. 110 (1969) 199-205.

T. Luczak and L. Pyber, On random generation of the symmetric group, Combin. Probab. Comput., 2 (1993), 505-512.

A. Maroti and C. M. Tamburini, Bounds for the probability of generating the symmetric and alternating groups, Arch. Math. (Basel), 96 (2011), 115-121.

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 A363011 A377359

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