论文标题
涉及Bernoulli数字和第二类的Stirling号码的身份
An identity involving Bernoulli numbers and the Stirling numbers of the second kind
论文作者
论文摘要
令$ b_ {n} $表示Bernoulli号码，而$ s（n，k）$表示第二类的stirling号码。我们证明以下身份$$ b_ {m+n} = \ sum _ {\ ordack {0 \ leq k \ leq n \\ 0 \ leq l \ leq l \ leq m}} \ frac {（ - 1） s（n，k）\，s（m，l）} {（k+l+1）\，\ binom {k+l} {l}}}。据我们所知，$$的身份是新的。
Let $B_{n}$ denote the Bernoulli numbers, and $S(n,k)$ denote the Stirling numbers of the second kind. We prove the following identity $$ B_{m+n}=\sum_{\substack{0\leq k \leq n \\ 0\leq l \leq m}}\frac{(-1)^{k+l}\,k!\, l!\, S(n,k)\,S(m,l)}{(k+l+1)\,\binom{k+l}{l}}. $$ To the best of our knowledge, the identity is new.
