On some series involving the binomial coefficients \binom3nn

2023/06/29 by Adegoke, Kunle, Frontczak, Robert, Goy, Taras
#11B39 #11B65 #40A05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.16889

Abstract

Using a simple transformation, we obtain much simpler forms for some series involving binomial coefficients \binom3nn derived by Necdet Batir. New evaluations are given; and connections with Fibonacci numbers and the golden ratio are established. Finally, we derive some Fibonacci and Lucas series involving the reciprocals of \binom3nn.

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