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Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations

H. A. Verrill
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Abstract

For a fixed integer N, and fixed numbers b_1,...,b_N, we consider sequences, the nth term (a_n) of which is the sum of the squares of the terms in the expansion of (b_1 + ... + b_N)^n. In the case all b_i=1, we give a formula for a recurrence relation for the a_n. 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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H. A. Verrill. 2004-07-19. Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations. https://arxiv.org/abs/math/0407327

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