\[B\left(n\right)={\mathrm{e}}^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!}=1+\left%
\lfloor{\mathrm{e}}^{-1}\sum_{k=1}^{2n}\frac{k^{n}}{k!}\right\rfloor.\]