According to wikipedia for different numbers $a_0, a_1, a_2,..., a_n$ we can write
$$f[a_0, a_1, a_2,...,a_n] = \sum_{j = 0}^n \frac{f(x_j)}{q'(x_j)}$$
where $q(x) = \prod_{i = 0}^n(x - x_i)$
Also, for the same numbers $(n + 1)$, we can write that:
$$f[a_0, a_0,...,a_0] = \frac{f^{(n)}(a_0)}{n!}$$
However, I'm wondering if we can write this expression in terms of polynomial $q$, as in the case of different nodes $a_0, a_1,...,a_n$. Could you please give a hand with justifying if its possible?