Let $X$ be a Kähler manifold of dimension $n$, and $Z \subset X$ an analytic subset of codimension $k$. I have read in a paper the following result, a proof of which I cannot find:

$$c_k(\mathscr{I}_Z) = (-1)^k(k-1)![Z]$$

The form of the expression suggests using GRR, but I cannot figure out how.

Does anyone know a proof for this (or at least an online reference)?