  Recently Richard Stanley initiated a study of the distribution of the length
as(w) of the longest alternating subsequence in a random permutation w from the
symmetric group $S_n$. Among other things he found an explicit formula for the
generating function (on n and k) for the probability that as(w) is at most k
and conjectured that the distribution, suitably centered and normalized, tended
to a Gaussian with variance 8/45. In this note we present a proof of the
conjecture based on the generating function.
