Advances in Applied Mathematics
The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for pm(n) for any desired m. We do this to demonstrate the power of “rigorous guessing” as facilitated by the quasi-polynomial ansatz.
Sills, Andrew, Doron Zeilberger.
"Formulæ for the Number of Partitions of n into at Most m Parts (Using the Quazi-Polynomial Ansatz)."
Advances in Applied Mathematics, 48 (5): 640-645.
doi: 10.1016/j.aam.2011.12.003 source: http://arxiv.org/abs/1108.4391