  The attractor equations for an arbitrary one-parameter family of Calabi-Yau
manifolds are studied in the large complex structure region. These equations
are solved iteratively, generating what we term an N-expansion, which is a
power series in the Gromov-Witten invariants of the manifold. The coefficients
of this series are associated with integer partitions. In important cases we
are able to find closed-form expressions for the general term of this
expansion. To our knowledge, these are the first generic solutions to attractor
equations that incorporate instanton contributions. In particular, we find a
simple closed-form formula for the entropy associated to rank two attractor
points, including those recently discovered. The applications of our solutions
are briefly discussed. Most importantly, we are able to give an expression for
the Wald entropy of black holes that includes all genus 0 instanton
corrections.
