2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131082We investigate a combinatorial sum that can be interpreted as the moments of a random variate, measuring the absolute distance to the origin in a symmetric Bernoulli random walk. These sums can be characterized by polynomials related to the Dumont-Foata polynomials. The sums corresponding to the odd moments have a connection to the Gandhi polynomials and Genocchi numbers.Related sequence in "The On-Line Encyclopedia of Integer Sequences" is A083061. See http://www.research.att.com/~njas/sequences/A083061Number TheoryStatistics Theory11B65; 60G50text