BBP formula for $e$

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For the number $\pi$ we can use the BBP formula to find a sequence of digit starting from the digit $n$, simply using the formula: $$\displaystyle\pi=\sum_{k=0}^\infty\dfrac{1}{16^k}\left(\dfrac{4}{8k+1}-\dfrac{2}{8k+4}-\dfrac{1}{8k+5}-\dfrac{1}{8k+6}\right).$$ Is there any similar formula able to calculate the $k$ digits after the $n^{th}$ for the base of natural logarithms $e$? Thanks