On Sums Related to Central Binomial and Trinomial Coefficients

DOI10.1007/978-1-4939-1601-6_18zbMath1339.11027arXiv1101.0600OpenAlexW1698404234MaRDI QIDQ5265402

Zhi-Wei Sun

Publication date: 23 July 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.0600

zbMATH Keywords

congruencesseries for \(1/\pi\)central binomial coefficientscentral trinomial coefficientsrepresentations of primes by binary quadratic forms

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Sums of squares and representations by other particular quadratic forms (11E25) Congruences; primitive roots; residue systems (11A07)

Related Items (12)

Supercongruences involving dual sequences ⋮ Congruences concerning generalized central trinomial coefficients ⋮ Arithmetic properties of Delannoy numbers and Schröder numbers ⋮ Some parametric congruences involving generalized central trinomial coefficients ⋮ Some new series for $1/\pi $ motivated by congruences ⋮ Legendre symbols related to certain determinants ⋮ Congruences involving squares of generalized central trinomial coefficients ⋮ New series for powers of \(\pi\) and related congruences ⋮ Polynomial reduction and supercongruences ⋮ Proof of some conjectural hypergeometric supercongruences via curious identities ⋮ On Motzkin numbers and central trinomial coefficients ⋮ Ramanujan-type \(1/\pi\)-series from bimodular forms

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