论文标题
通过新的身份和其他结果获得的种族基数的完整性
The integrality of the Genocchi numbers obtained through a new identity and other results
论文作者
论文摘要
在本说明中，我们研究了常规项$ a_n的整数序列的一些属性：= \ sum_ {k = 0}^{n -1} k！ （n -k -k -1）！$（$ \ forall n \ geq 1 $）得出genocchi数字的新身份$ g_n $（$ n \ in \ mathbb {n} $），这立即表明$ g_n \ in \ mathbb {z} $ in \ mathbb {z} $ in \ in \ mathbbbbbbbbbb {n} $。在另一个方向上，我们获得了合理数字的$ 2 $ -ADIC估值$ \ sum_ {k = 1}^{n} \ frac {2^k} {k} $。
In this note, we investigate some properties of the integer sequence of general term $a_n := \sum_{k = 0}^{n - 1} k! (n - k - 1)!$ ($\forall n \geq 1$) to derive a new identity of the Genocchi numbers $G_n$ ($n \in \mathbb{N}$), which immediately shows that $G_n \in \mathbb{Z}$ for any $n \in \mathbb{N}$. In another direction, we obtain nontrivial lower bounds for the $2$-adic valuations of the rational numbers $\sum_{k = 1}^{n} \frac{2^k}{k}$.
