Some recurrences for sums of powers of binomial coefficients
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).
scientific article; zbMATH DE number 4016989