  The theme of the article is the study of the unipotent part of Arthur's trace
formula for general linear groups. The case of regular (or "regular by blocks")
unipotent orbits has been essentially done in a previous paper. Here we are
interested by the contribution of Richardson orbits that are induced by Levi
subgroups with two-by-two distinct blocks. In this case, the contribution is
remarkably given by a global unipotent weighted orbital integral. As a
corollary, we get integral formulas for some of Arthur's global coefficients.
We also present a new construction of Arthur's local unipotent weighted orbital
integral.
