Septaphobia

Calculus Level 3

171!+17+272!+17+27+373!+17+27+37+474!+ \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

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

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

Inspired by Caleb Townsend

Image Credit: Flickr Gingertwist
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