  In his book \emph{Topics in Analytic Number Theory}, Hans Rademacher
conjectured that the limits of certain sequences of coefficients that arise in
the ordinary partial fraction decomposition of the generating function for
partitions of integers into at most $N$ parts exist and equal particular values
that he specified. Despite being open for nearly four decades, little progress
has been made toward proving or disproving the conjecture, perhaps in part due
to the difficulty in actually computing the coefficients in question.
  In this paper, we provide a fast algorithm for calculating the Rademacher
coefficients, a large amount of data, direct formulas for certain collections
of Rademacher coefficients, and overwhelming evidence against the truth of the
conjecture. While the limits of the sequences of Rademacher coefficients do not
exist (the sequences oscillate and attain arbitrarily large positive and
negative values), the sequences do get very close to Rademacher's conjectured
limits for certain (predictable) indices in the sequences.
