2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67794We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack polynomials. These quantities are the moments of the "alpha-content" random variable with respect to some transition probability distributions.22 pages, LaTeX, to appear in Trans. Amer. Math. SocCombinatorics05A10, 05A17, 05E05, 33C52, 33C80text