Recurrence relation associated with the sums of square binomial coefficients

Abstract

Our purpose is to describe the recurrence relation associated to the sums of diagonal elements lying along a finite ray of square binomial triangle. We also give the generating function. As consequences of the main theorem we prove some recurrence relations conjectured in Sloane’s OEIS, furthermore we also give some combinatorial identities.

Key words: Recurrence relation, generating function, square binomials.