@article{Yang2023, 
author = {Jizhen Yang and Yunpeng Wang},
title = {Congruences involving generalized Catalan numbers and Bernoulli numbers},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {24331-24344},
keywords = {Bernoulli numbers, congruences, generalized Catalan numbers, generalized harmonic numbers},
url = {https://www.sciopen.com/article/10.3934/math.20231240},
doi = {10.3934/math.20231240},
abstract = {In this paper, we establish some congruences mod        p    3   involving the sums        ∑          k      =      1              p      −      1            k    m        B          p      ,      k              2      l      , where    p  >  3 is a prime number and        B          p      ,      k       are generalized Catalan numbers. We also establish some congruences mod        p    2   involving the sums        ∑          k      =      1              p      −      1            k    m        B          p      ,      k              2              l        1                  B          p      ,      k      −      d              2              l        2            , where    m  ,      l    1    ,      l    2    ,  d are positive integers and    1  ≤  d  ≤  p  −  1.}
}