The Dubov-Eleonskii-Kulagin polynomials and a modification of the Christoffel formula

In this note we demonstrate that the polynomials introduced by Dubov, Eleonskii, and Kulagin in relation to nonharmonic oscillators with equidistant spectra are a discrete Darboux transformation of Hermite polynomials. In particular, we obtain a modification of the Christoffel formula since its classical form cannot be applied in this case.