  We construct a special family of equivariant coherent sheaves on the Hilbert
scheme on $n$-points in the affine plane. The equivariant Euler characteristic
of these sheaves are closely related to the symmetic functions $(-1)^{n-1}
\nabla p_n$. We prove a higher cohomology vanishing result of these sheaves. It
follows from the Bridgeland-King-Reid correspondence that there is an effective
$S_n$ module underlying the aforementioned family of symmetric functions.
