In one of my old (Dutch) algebra/analysis problem books, I came across the following "cute" double sum identity:
n∑k=1k∑h=1h2−3h+1h!=−n−1+1n!,
which the reader was asked to prove true for all n∈N. The proof is relatively straightforward, with induction on n. (Although I'd love to see a more imaginative proof!)
My question is, can we somehow generalise this identity? Because this is a rather non-obvious result, I have a hunch that the textbook writer derived it from some more general theorem. But I have no idea what to look for.
Any insights will be warmly appreciated!
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