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

Offset: 3

Author

Dan Hoey

Keywords

• nonn
• more
• nice

Comments

Probability is A040173(n)/A040174(n) = a(n)/n!.

Note that a(2)=3/2 is not integer.

Examples

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

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

• 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. Łuczak 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.

Crossrefs

Cf. A040173, A040174, A071605, A135474.

Formula

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

Extensions

Edited by Max Alekseyev, Jan 28 2012

a(10)-a(13) from Stephen A. Silver, Feb 21 2013