  We work in the context of the infinitely many alleles model. The allelic
partition associated with a coalescent process started from n individuals is
obtained by placing mutations along the skeleton of the coalescent tree; for
each individual, we trace back to the most recent mutation affecting it and
group together individuals whose most recent mutations are the same. The number
of blocks of each of the different possible sizes in this partition is the
allele frequency spectrum. The celebrated Ewens sampling formula gives precise
probabilities for the allele frequency spectrum associated with Kingman's
coalescent. This (and the degenerate star-shaped coalescent) are the only
Lambda coalescents for which explicit probabilities are known, although they
are known to satisfy a recursion due to Moehle. Recently, Berestycki,
Berestycki and Schweinsberg have proved asymptotic results for the allele
frequency spectra of the Beta(2-alpha,alpha) coalescents with alpha in (1,2).
In this paper, we prove full asymptotics for the case of the
Bolthausen-Sznitman coalescent.
