Triple Cripple(Calculus Challenge 10)!

Level pending

\(\displaystyle \left \lfloor 10 \sum_{n=0}^{\infty}{\frac{1}{n!!!}}\right \rfloor = ?\)

Challenge

Generalize for \(\displaystyle \sum_{n=0}^{\infty}{\frac{1}{n!^{(k)}}}\), where \(n!^{(k)}\) is the \(k\)th multifactorial.

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