  A recently formulated conjecture of Gamayun, Iorgov and Lisovyy gives an
asymptotic expansion of the Jimbo--Miwa--Ueno isomonodromic $\tau$-function for
certain Painlev\'e transcendents. The coefficients in this expansion are given
in terms of conformal blocks of a two-dimensional conformal field theory, which
can be written as infinite sums over pairs of partitions. In this note a
discrete matrix model is proposed on a lattice whose partition function can be
used to obtain a multiple integral representation for the length restricted
partial sums of the Painlev\'e conformal blocks. This leads to expressions of
the partial sums involving H\"ankel determinants associated to the discrete
measure of the matrix model, or equivalently, Wronskians of the corresponding
moment generating function which is shown to be of the generalized
hypergeometric type.
