Let's do some calculus! (41)

Calculus Level 5

\[\large \displaystyle \sum_{n=1}^{\infty} {(-1)}^{n-1} \dfrac{n^8}{n!} = \dfrac ke\]

What is \(| k | \)?

Notations:

\(e \approx 2.71828\) denotes the Euler's number.
\( | \cdot | \) denotes the absolute value function.

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