@article{Chen2024, 
author = {Kwang-Wu Chen and Fu-Yao Yang},
title = {Infinite series involving harmonic numbers and reciprocal of binomial coefficients},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {16885-16900},
keywords = {multiple zeta values, harmonic numbers, binomial coefficients, Yamamoto's integral, 2-poset},
url = {https://www.sciopen.com/article/10.3934/math.2024820},
doi = {10.3934/math.2024820},
abstract = {Yamamoto's integral was the integral associated with 2-posets, which was first introduced by Yamamoto. In this paper, we obtained the values of infinite series involving harmonic numbers and reciprocal of binomial coefficients by using some techniques of Yamamoto's integral. We determine the value of infinite series of the form:         ∑                  m        1            ,      …      ,              m        n            ,              ℓ        1            ,      …      ,              ℓ        k            ≥      1                          H                              m            1                                    (                      a            1                    )                    ⋯              H                              m            n                                    (                      a            n                    )                                    m        1                              b            1                              ⋯              m        n                              b            n                                      ℓ        1                              c            1                              ⋯              ℓ        k                              c            k                                                (                                                    m              1                        +            ⋯            +                          m              n                        +                          ℓ              1                        +            ⋯            +                          ℓ              k                                            ℓ            k                                    )                      ,in terms of a finite sum of multiple zeta values, for positive integers        a    1    ,  …  ,      a    n    ,      b    1    ,  …  ,      b    n    ,      c    1    ,  …  ,      c    k  .}
}