I am having trouble evaluating the following finite sum:
$$ \sum_{l=0}^{r}\binom{r}{l}(r-l)^{k},\qquad k\in\mathbb{N}_{0}. $$
Can you shed light on it?
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5Are you be able to evaluate $\sum_{l=0}^r {r\choose l} l^k$? – Casteels Dec 18 '14 at 10:38
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Yes... this finite sum involves Stirling numbers... – Axl Dec 18 '14 at 10:43
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3Ok great. Because it's the same sum! – Casteels Dec 18 '14 at 10:51
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Wow, it's true! What a silly question I have posted! Thank you :) – Axl Dec 18 '14 at 11:08
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Resembles http://math.stackexchange.com/questions/591350/factorial-as-difference-of-powers-sum-r-0n-binomnr-1rl-rn-n – lab bhattacharjee Dec 18 '14 at 12:36