[seqfan] Re: Two Sequences Related To Permutations of (1,2,...,n)

[Edwin Clark]

On Sat, 17 Jan 2009, Leroy Quet wrote:

> (1)
>
> Let a(n) = the number of permutations (p(1),p(2),p(3)...,p(n)) of (1,2,3,...,n) where, if each (m,p(m)) is plotted on a graph, then the entire set P of the n of these plotted points would be on the perimeter of the convex hull of P.
>
> For instance, for n = 5:
>
> (p(1),p(2),p(3),p(4),p(5)) = (1,3,5,2,4) would be included in the count, but
> (1,4,3,2,5) would not because point (3,3) is not on the perimeter of the convex hull of P.
>

Isn't this the same as

http://www.research.att.com/~njas/sequences/A000079

...number of weakly unimodal permutations of 1..n, that is, permutations 
with exactly one local maximum.

If so the formula is 2^(n-1).