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.

For more problems on calculus, click here.