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Closed form or/and asymptotics of a hypergeometric sum
Dear mathematicians,
I am a computer scientist wandering in the deep sea of combinatorics and asymptotics to pursue a recent interest in average case analysis of algorithms. In doing so, I designed ...
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3
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Is the sum $\sum\limits_{j=0}^{k-1}(-1)^{j+1}(k-j)^{2k-2} \binom{2k+1}{j} \ge 0?$
I am trying to prove $\sum\limits_{j=0}^{k-1}(-1)^{j+1}(k-j)^{2k-2} \binom{2k+1}{j} \ge 0$. This inequality has been verified by computer for $k\le40$.
Some clues that might work (kindly provided by ...
