The rascal triangle, a clever play on Pascal's triangle, was defined recursively by Anggoro et al., and has since been studied by many others. We assign two combinatorial interpretations to the elements of the rascal triangle, and these elements are dubbed the rascal numbers. The first combinatorial interpretation of the rascal numbers involves counting ascents in binary words; the second interpretation involves pattern avoidance in the ascent sequences studied by Duncan and Steingrímsson and is directly related to a more recent paper by Baxter and Pudwell. We provide many new Pascal-like formulas involving rascal numbers, and we conclude with a natural generalization of these numbers.