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The purpose of this short article is to announce, and briefly describe, aMaple package, PARTITIONS, that (inter alia) completely automaticallydiscovers, 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 "rigorousguessing" as facilitated by the quasi-polynomial ansatz.

Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)