2018/07/22 by Johann Cigler, Cigler, Johann, Mike Tyson +1
Mathematics · #05A10 #11B39 #11C20 #15B36 #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1807.08330
openalex publication_date 2018/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For small r the Hankel determinants dr(n) of the sequence (2n+r\choose n)n≥ 0 are easy to guess and show an interesting modular pattern. For arbitrary r and n no closed formulae are known, but for each positive integer r the special values dr(rn), dr(rn+1), and dr(rn+\lfloor(r+1)/(2)\rfloor) have nice values which will be proved in this paper.