Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations
Abstract
For a fixed integer N, and fixed numbers b1,...,bN, we consider sequences, the nth term (an) of which is the sum of the squares of the terms in the expansion of (b1 + ... + bN)n. In the case all bi=1, we give a formula for a recurrence relation for the an. Otherwise we give an algorithm for finding a recurrence relation. As an application, we give the Picard-Fuchs equations for certain families of elliptic curves.
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