2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101336We show that the sum of the four parameter weights over all ordinary or strict partitions with parts each less than or equal to a given integer $N$ is expressed by the Al-Salam Chihara polynomials. This weight is a generalization of the Andrews-Stanley partition function. As a corollary we prove C. Boulet's results when the sum runs over all ordinary or strict partitions. In the last section we study the weighted sum of Schur's $P$-functions and $Q$-functions, where the sum runs over all strict partitions.25 pagesCombinatoricsRepresentation Theory05E05 (Primary) 05A17, 05A30, 05E35, 33D15, 33D45 (Secondary)text