[What does A040174 mean?]

[Christian G.Bower]

Joe Crump <joecr at microsoft.com> wrote:
---------------
Hi,

	Can someone help me understand the description of A040174?
What does it mean, or how is it calculated? I think I'm just not familiar
with the terminology.

	Here's the entry for reference:
----------------------------------------------------------------------------
--------------------------------------------------------
ID Number: A040174
Sequence:  1,2,2,8,40,120,168,6720,120960
Name:      Denominator of probability that 2 elements of S_n chosen at
random
           (with replacement) generate S_n.
[snip]
------------

S_n is the symmetric group over a set of n elements.
In other words it's a group (if you don't know what that is, it will
take a little while to explain) with n! elements which are all the
permutations (or one to one, onto functions) of the set of n elements.
The multiplication of the group is composition of functions.

The title of the sequence states that it's the probabilty that if you
chose two of the n! elements at random (with the possibility of choosing
the same element twice, hence the with replacement) that those
two elements would generate the entire symmetric group, i.e. you can
get every element of the group through products of those two.


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