2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62780We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence $a_{i,j}=a_{i-1,j}+a_{i,j-1}$, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland Bacher [J. Théorie Nombres Bordeaux 13 (2001), to appear; see http://arxiv.org/abs/math.CO/0109013].19 pages, AmS-TeXCombinatoricsNumber TheoryRings and Algebras05A19 (Primary) 05A10 11C20 15A15 33C45 (Secondary)text