Find the number of permutations of (1,2,3...n) possessing the following feature:

The number n is the only local maximum e.g. 123465, 123564, 654321,
as opposed to 651432, 261354.

(In reply to solution by Charlie)

Of course the result is true and nicely explained.

Still, there is a significantly shorter simple proof.

I will publish it within few days, allowing solvers to give it a trial.

Posted by Ady TZIDON on 2015-10-02 00:00:20