Title of article :
Convolution identities involving the central binomial coefficients and Catalan numbers
Author/Authors :
Batır, Necdet Department of Mathematics - Nev sehir Hacı Bekta - s Veli University, Turkey , Kucuk, Hakan Department of Mathematics - Nev sehir Hacı Bekta - s Veli University, Turkey , Sorgun, Sezer Department of Mathematics - Nev sehir Hacı Bekta - s Veli University, Turkey
Abstract :
We generalize some convolution identities due to Witula and Qi et al. involving the central binomial coefficients and Catalan numbers. Our formula allows us to establish many new identities involving these important quantities, and recovers some known identities in the literature. Also, we give new proofs of Shapiro's Catalan convolution and a famous identity of Haj'{o}s.
Keywords :
Convolution Identity , Combinatorial Identity , Central Binomial Coefficient , Catalan Number , Harmonic Number
Journal title :
Transactions on Combinatorics
