Some recurrences for sums of powers of binomial coefficients (Q580400)
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scientific article; zbMATH DE number 4016989
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some recurrences for sums of powers of binomial coefficients |
scientific article; zbMATH DE number 4016989 |
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Some recurrences for sums of powers of binomial coefficients (English)
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1987
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Using MACSYMA the author gives for \(r=5,6\) a recurrence relation between the terms of the sequence \(\sum^{n}_{k=0}\left( \begin{matrix} n\\ k\end{matrix} \right)^ r\). This extends earlier results with \(r=2,3,4\). Such recurrences aroused some interest several years ago in connection with Apéry's irrationality proof for \(\zeta\) (3).
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four-term recurrences
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sums of powers of binomial coefficients
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MACSYMA
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recurrence relation
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