What does A040174 mean?

[Joe Crump]

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:
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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.
See also:  Cf. A040174-A040176.
Keywords:  nonn,frac
Offset:    1
Author(s): Dan Hoey (Hoey at aic.nrl.navy.mil)
----------------------------------------------------------------------------
--------------------------------------------------------

	It seems related to n factorial (perhaps divided by gcd with
original numerator?).
Also, is there a known formula for this sequence?

Thanks!

- Joe

Btw: The cross-reference on A040174 points to itself, rather than A040175.