A determinantal form for Δ
h
‐Appell sequences is proposed and general properties are obtained by using elementary linear algebra tools. As particular cases of Δ
h
‐Appell sequences the sequence of Bernoulli polynomials of second kind and the one of Boole polynomials are considered. A general linear interpolation problem, which generalizes the classical interpolation problem on equidistant points, is proposed. The solution of this problem is expressed by a basis of Δ
h
‐Appell polynomials. Numerical examples which justify theoretical results on the interpolation problem are given.
