Dependent types are a key feature of the proof assistants based on the Curry-Howard isomorphism. It is well known that this correspondence can be extended to classical logic by enriching the language of proofs with control operators. However, they are known to misbehave in the presence of dependent types, unless dependencies are restricted to values. Moreover, while sequent calculi naturally support continuation-passing-style interpretations, there is no such presentation of a language with dependent types. The main achievement of this article is to give a sequent calculus presentation of a call-by-value language with a control operator and dependent types, and to justify its soundness through a continuation-passing-style translation. We start from the call-by-value version of the λμ˜μ -calculus. We design a minimal language with a value restriction and a type system that includes a list of explicit dependencies to maintain type safety. We then show how to relax the value restriction and introduce delimited continuations to directly prove the consistency by means of a continuation-passing-style translation. Finally, we relate our calculus to a similar system by Lepigre and present a methodology to transfer properties from this system to our own.