On a New Alternating Convolution Formula for the Super Catalan Numbers

Abstract

We present a new alternating convolution formula for the super Catalan numbers which arises as a generalization of two known binomial identities. We prove a generalization of this formula by using auxiliary sums, recurrence relations, and induction. By using a new method, we prove one interesting divisibility result with super Catalan numbers.

arXiv comment21 pages

References in corpus (2)

• A Combinatorial Interpretation of The Numbers $6(2n)!/n!(n+2)!$
• Alternating Convolutions of Catalan Numbers