On the powers of Motzkin paths.
An extension of the Ramanujan-Bailey formula. (Une extension d'une formule de Ramanujan-Bailey.)
The Akiyama-Tanigawa algorithm for Carlitz's -Bernoulli numbers.
Two involutions for signed excedance numbers.
Generalization of Waring-type formulas. (Généralisation de formules de type Waring.)
On an extension of Euler numbers and records of alternating permutations. (Sur une extension des nombres d'Euler et les records des permutations alternantes.)
Some equidistributed statistics on Genocchi permutations.
Distribution of crossings, nestings and alignments of two edges in matchings and partitions.
Combinatorial interpretations of the Jacobi-Stirling numbers.
On some analogues of descent numbers and major index for the hyperoctahedral group.
On the total weight of weighted matchings of segment graphs.
A -analogue of Faulhaber's formula for sums of powers.
Combinatorial proof of a curious -binomial coefficient identity.
The combinatorics of the Al-Salam-Chihara -Charlier polynomials.
On a generalization of binomial coefficients. (Sur une généralisation des coefficients binomiaux.)
A combinatorial proof of a symmetric -Pfaff-Saalschütz identity.
Derangements and Euler's difference table for .
New Euler-Mahonian permutation statistics.
Further results on the Euler and Genocchi numbers.
Some q-supercongruences for truncated basic hypergeometric series
For any odd prime p we obtain q-analogues of van Hamme’s and Rodriguez-Villegas’ supercongruences involving products of three binomial coefficients such as for p≡ 3 (mod 4), for p≡ 2 (mod 3), where and . We also prove q-analogues of the Sun brothers’ generalizations of the above supercongruences. Our proofs are elementary in nature and use the theory of basic hypergeometric series and combinatorial q-binomial identities including a new q-Clausen type summation formula.
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