\[ \frac {1^7}{1!} + \frac {1^7 + 2^7}{2!} + \frac {1^7 + 2^7 + 3^7}{3!} + \frac {1^7 + 2^7 + 3^7 + 4^7}{4!} + \ldots \]
###### Image Credit: Flickr Gingertwist

If the series above equals to \(W\), what is the value of \(\frac {24}{e} \times W \)?

Note: \(e = \displaystyle \lim_{n \to \infty} \left (1 + \frac 1 n \right )^n \)

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