[seqfan] double factorial division

[Anchar Koops]

Dear all,



I found an interesting sequence that is not in the OEIS. It is like
factorial but with division instead e.g. input 4 would give 4/ (3/ (2/1)) =
2,666…

Or:

output = n / ((n-1) / ((n-2) / ((n-3) / ... / (3/ (2/1))…)))


I was happy to find it can also be written as:

output = n!! / (n-1)!!



These are the first 10 possible positive integer inputs:

n             output                  |output|

1             1,00                      1

2             2,00                      2

3             1,50                      2

4             2,67                      3

5             1,88                      2

6             3,20                      3

7             2,19                      2

8             3,66                      4

9             2,46                      2

10           4,06                      4



As you can see the output oscillates. However, some start inputs e.g.
1,3992863… create a line.



I cannot imagine this has not been found many times before. Is this
sequence worthy?



Thank you very much for your attention.
Anchar