关于整数的两类加权幂和(英文)

ON TWO KINDS OF WEIGHTED SUMS OF POWERS OF INTEGERS

本文研究了n个自然数的m农幂分别以与（k=1，2…，n）为权的两类加权和。文中给出了和式的形式较为简单的递推公式；利用第二类Stirling数求出了和式的一般闭型表达式；同时，研究了和式的结构特征，并由此给出了和式的某些整除性质．

In this paper we deal with two kinds of summations of the first n positive integers weighted by () and () (k =1, 2,…,n), respectively. Some simpler recurrences of the summations are given; The general closed forms of the summations are founded by using the Stirling numbers of the second kind, Besides, the structure characteristics of the summations are considered, and some divisibilities of them are also given.