What does A040174 mean?

[Michael Somos]

Joe Crump asked about A040174. This seems to be one of a set of three
related sequences. That is, A040173-A040175 are all related. They are :

%S A040173 1,1,1,3,19,53,103,4111,78293
%N A040173 Numerator of probability that 2 elements of S_n chosen at random ...

%S A040174 1,2,2,8,40,120,168,6720,120960
%N A040174 Denominator of probability that 2 elements of S_n chosen at random ...

%S A040175 1,1,3,9,57,318,3090,24666,234879
%N A040175 n! times probability that 2 elements of S_n chosen at random ...

gp> for(n=1,9,print(n" "an[n]" "numerator(an[n]/n!)" "denominator(an[n]/n!)))
1 1 1 1
2 1 1 2
3 3 1 2
4 9 3 8
5 57 19 40
6 318 53 120
7 3090 103 168
8 24666 4111 6720
9 234879 78293 120960

As to whether the numbers are correct, I have not studied that yet. Shalom,
Michael

-- 
Michael Somos <somos at grail.cba.csuohio.edu>     Cleveland State University
http://grail.cba.csuohio.edu/~somos/            Cleveland, Ohio, USA 44115