Summary: We provide new formulas for the coefficients in the partial fraction decomposition of the restricted partition generating function. These techniques allow us to partially resolve a recent conjecture of A. V. Sills and D. Zeilberger [J. Difference Equ. Appl. 19, No. 4, 680–689 (2013; Zbl 1301.11069)]. We also describe upcoming work, giving a resolution to Rademacher’s conjecture on the asymptotics of these coefficients.