How to estimate from above the following sums: $$ \sum_{i=0}^K \sum_{j=0}^{L-K}\binom{K}{i}\binom{L-K}{j} (-1)^i (L-2i-2j)^N $$
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Not sure if it helps much, but you can rewrite it as $$\sum_{r=0}^{L}\left(\sum_{i=0}^{K}\binom{K}{i}\binom{L-K}{r-i}(-1)^i\right)(L-2r)^N.$$ – Alexander Burstein Feb 04 '22 at 09:53
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1Don't know if this might help. – Fabius Wiesner Feb 04 '22 at 16:26
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I might help to add some context, how you got this sum? – leonbloy Feb 08 '22 at 14:07
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Thank you. It was a game of some probability sums. Technically calculation of an odd and even pairs of numbers. The content would not help much... – volond Feb 08 '22 at 15:18