You gotta love 13.

\[ \large \sum_{r=1}^{12} (-1)^r r^{13} \dbinom{12}r = \, ? \]

Bonus: Generalized it for \(\displaystyle \sum _{ r=1 }^{ n }{ [{ (-1) }^{ r }{ r }^{ n+1 } } (_{ r }^{ n })]\).

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