On sums of binomial coefficients involving Catalan and delannoy numbers modulo \(p^2\)

DOI10.1007/s11139-016-9853-6zbMath1433.11016OpenAlexW2579837795MaRDI QIDQ682001

Guo-Shuai Mao

Publication date: 13 February 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-016-9853-6

zbMATH Keywords

congruencesCatalan numbersharmonic numbersDelannoy numberscentral binomial coefficients

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Congruences; primitive roots; residue systems (11A07)

Related Items (1)

Proof of some supercongruences via the Wilf–Zeilberger method

Cites Work

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• On congruences related to central binomial coefficients
• On Delannoy numbers and Schröder numbers
• Generalized Legendre polynomials and related supercongruences
• Congruences for central binomial sums and finite polylogarithms
• A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.
• Super congruences and Euler numbers
• A combinatorial identity with application to Catalan numbers
• On sums of binomial coefficients modulo p²
• A new series for π³and related congruences
• Congruences concerning Legendre polynomials
• Congruences for the second-order Catalan numbers
• Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs

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