[seqfan] question about A006694

[jean-paul allouche]

Dear Seqfans

There is a comment at the beginning of http://oeis.org/A006694
saying:

>>>>> The number of cycles in permutations constructed from siteswap
juggling patterns 1, 123, 12345, 1234567, etc., i.e., the number
of ball orbits in such patterns minus one.
>>>>> 
Does anyone know a paper or book where this is explained/proved
explicitly? Being bad at both juggling and the mathematics of juggling,
I would prefer not to learn thoroughly both the details of the theory and
a high-level practice :-)


PS I did not find the answer in the book of F. J. MacWilliams and N. J. 
A. Sloane,
     nor in the book "Mathematics of Juggling" by B. Polster, which, by 
the way,
     contains a nice chapter on bell ringing and its links with juggling 
--which might
     lead to a similar question.

many thanks in advance
best wishes
jean-paul