Which of the following series diverges?

A: \(\displaystyle \sum\limits_{n\in\mathbb{Z^+}} \frac{n^4-\frac{1}{4}}{4^n+\log4}\)

B: \(\displaystyle \sum\limits_{n\in\mathbb{Z^+}} (\frac{n^2+3n}{4n^5+6})^n\)

C: \(\displaystyle \sum\limits_{n\in\mathbb{Z^+}} \frac{5\sin(n)+12\cos(n)}{13e^n}\)

D: \(\displaystyle \sum\limits_{n\in\mathbb{Z^+}} \frac{e(n!)}{e^n-n^e}\)

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