  The ellipsoidal superpotential of the complex projective plane can be
interpreted as a count of rigid rational plane curves of a given degree with
one prescribed cusp singularity. In this note we present a closed formula for
these counts as a sum over trees with certain explicit weights. This is a step
towards understanding the combinatorial underpinnings of the ellipsoidal
superpotential and its mysterious nonvanishing and nondecreasing properties.
