Acyclic orientations and chromatic generating functions

Let P(k) be the chromatic polynomial of a graph with n⩾2 vertices and no isolated vertices, and let R(k)=P(k+1)/k(k+1). We show that the coefficients of the polynomial (1−t)n−1∑k=1∞ R(k)tk are nonnegative and we give a combinatorial interpretation to R(k) when k is a nonpositive integer.