  We present a robust method which translates information on the speed of
coming down from infinity of a genealogical tree into sampling formulae for the
underlying population. We apply these results to population dynamics where the
genealogy is given by a Lambda-coalescent. This allows us to derive an exact
formula for the asymptotic behavior of the site and allele frequency spectrum
and the number of segregating sites, as the sample size tends to infinity. Some
of our results hold in the case of a general Lambda-coalescent that comes down
from infinity, but we obtain more precise information under a regular variation
assumption. In this case, we obtain results of independent interest for the
time at which a mutation uniformly chosen at random was generated. This
exhibits a phase transition at \alpha=3/2, where \alpha \in(1,2) is the
exponent of regular variation.
