On Divisibility of Convolutions of Central Binomial Coefficients

[摘要] Recently, Z. Sun proved that \[ 2(2m+1)\binom{2m}{m} \mid  \binom{6m}{3m}\binom{3m}{m} \] for $m\in\mathbb{Z}_{>0}$. In this paper, we consider a generalization of this result by defining \[ b_{n,k}=\frac{2^{k}\, (n+2k-2)!!}{((n-2)!!\, k!}. \] In this

[学科分类] 离散数学和组合数学

[关键词] central binomial coefficients