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
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.