We consider the family of polynomials
$$\left\{ \begin{array}{l} H_0 = 1 \\ H_k = \frac{1}{k!} \prod_{j=0}^{k-1} (X - j) \quad \text{for } k \in \llbracket 1, n \rrbracket \end{array} \right.$$
Show that $P \in \mathbb{R}_n[X]$ is integer-valued on the integers if and only if its coordinates in the basis $\left(H_k\right)_{k \in \llbracket 0, n \rrbracket}$ are integers.