  We investigate the prepotential that describes certain F^4 couplings in eight
dimensional string compactifications, and show how they can be computed from
the solutions of inhomogenous differential equations. These appear to have the
form of the Picard-Fuchs equations of a fibration of Sym^2(K3) over P^1. Our
findings give support to the conjecture that the relevant geometry which
underlies these couplings is given by a five-fold.
