  We quantify the manner in which the beta coalescent $\Pi=\{ \Pi(t), t\geq
0\},$ with parameters $a\in (0, 1),$ $b>0,$ comes down from infinity.
Approximating $\Pi$ by its restriction $\Pi^n$ to $[n]\:= \{1, \ldots, n\},$
the suitably rescaled block counting process $n^{-1}\#\Pi^n(tn^{a-1})$ has a
deterministic limit, $c(t)$, as $n\to\infty.$ An explicit formula for $c(t)$ is
provided in Theorem 1.
  The block size spectrum $(\mathfrak{c}_{1}\Pi^n(t), \ldots,
\mathfrak{c}_{n}\Pi^n(t)),$ where $\mathfrak{c}_{i}\Pi^n(t)$ counts the number
of blocks of size $i$ in $\Pi^n(t),$ captures more refined information about
the coalescent tree corresponding to $\Pi$. Using the corresponding rescaling,
the block size spectrum also converges to a deterministic limit as
$n\to\infty.$ This limit is characterized by a system of ordinary differential
equations whose $i$th solution is a complete Bell polynomial, depending only on
$c(t)$ and $a,$ that we work out explicitly, see Corollary 1.
