Multiple Sums of Circular Binomial Products

Abstract

Five classes of multiple sums about circular products of binomial coefficients are investigated. Their generating functions are explicitly expressed as rational functions, with coefficients being Fibonacci and Lucas numbers. This is fulfilled by a novel approach called “recursive construction”, which also permits us to establish, for the circular sums, both generating functions and recurrence relations through the Lagrange expansion formula.

Keywords

• binomial coefficient
• generating function
• Fibonacci number
• Lucas number
• circular sum