  The generating function for $p_N(n)$, the number of partitions of $n$ into at
most $N$ parts, may be written as a product of $N$ factors. We find the
behavior of coefficients in the partial fraction decomposition of this product
as $N \to \infty$ by applying the saddle-point method, where the saddle-point
we need is associated to a zero of the analytically continued dilogarithm. Our
main result disproves a conjecture of Rademacher.
