2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164850Let S(n,k) be the Stirling number of the second kind. Wilf conjectured that the alternating sum of S(n,k) for k from 0 to n is not zero for all n>2. In this paper, we prove that Wilf conjecture is true except at most one number with the properties of weighted Motzkin number.7 pages, draft versionCombinatoricsNumber Theory11B73 (Primary) 05A18 (Secondary)text