2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230776The Jacobi-Stirling numbers of the first and second kinds were introduced in 2006 in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers. Andrews and Littlejohn have recently given a combinatorial interpretation for the second kind of the latter numbers. Noticing that these numbers are very similar to the classical central factorial numbers, we give combinatorial interpretations for the Jacobi-Stirling numbers of both kinds, which provide a unified treatment of the combinatorial theories for the two previous sequences and also for the Stirling numbers of both kinds.15 pagesCombinatoricsClassical Analysis and ODEs05A05, 05A15, 33C45 (Primary); 05A10, 05A18, 34B24 (Secondary)text