The number of points x that lie in an integer cube C and satisfies certain constraints is approximated by an Edgeworth corrected gaussian approximation based on the maximum entropy density on C, that satisfies the constraints in expectation . The asymptotic validity of the Edgeworth corrected estimate is proved and demonstrated for counting contingency tables with given row sums as the number of rows and columns approaches infinity, and demonstrated for counting the number of graphs with a given degree sequence, as the number of vertices approaches infinity.
