论文标题
在一个好奇的整数序列上
On a curious integer sequence
论文作者
论文摘要
该注释专门研究以下定义的复发数值序列：$ a_0 = 0 $，$ a_n = \ frac {n} {2} a_ {n -1} +（n -1） +（n -1）！$（$ \ forall n \ geq 1 $）。虽然，$ {（a_n）} _ n $立即由有理数构成，分母的功率为$ 2 $，但$ {（a_n）} _ n $实际上是一个整数序列并不微不足道。在本说明中，我们通过在Genocchi数字和第一类的Stirling数字方面表达$ A_N $来证明这一事实。我们从我们的主要结果中得出了几个推论，并以一些言论和开放的问题得出结论。
This note is devoted to study the recurrent numerical sequence defined by: $a_0 = 0$, $a_n = \frac{n}{2} a_{n - 1} + (n - 1)!$ ($\forall n \geq 1$). Although, it is immediate that ${(a_n)}_n$ is constituted of rational numbers with denominators powers of $2$, it is not trivial that ${(a_n)}_n$ is actually an integer sequence. In this note, we prove this fact by expressing $a_n$ in terms of the Genocchi numbers and the Stirling numbers of the first kind. We derive from our main result several corollaries and we conclude with some remarks and open problems.
