The dual Hilbert-Samuel function of a Maximal Cohen-Macaulay module

Let $R$ be a Cohen-Macaulay local ring with a canonical module $omega_R$. Let $I$ be an $m$-primary ideal of $R$ and $M$, a maximal Cohen-Macaulay $R$-module. We call the function $nlongmapsto ell (Hom_R(M,{omega_R}/{I^{n+1} omega_R}))$ the dual Hilbert-Samuel function of $M$ with respect to $I$. By a result of Theodorescu this function is a polynomial function. We study its first two normalized coefficients.