  We consider labeled $r$-uniform hypertrees having $n \ge r \ge 2$ vertices.
The number of hyperedges in such a hypertree is $m = (n - 1)/(r - 1)$. We show
that there are exactly $f(n, r) = \frac{(n-1)! n^{m-1}}{(r-1)!^m m!}$
$r$-uniform hypertrees with $n$ vertices labeled with distinct integers. We
also give an encoding scheme that encodes such hypertrees using, on an average,
at most $1 + \log_2 e$ bits more than $\log_2(f(n, r))$.
