On recurrences for sums of powers of binomial coefficients
The authors prove that for \(r\geq 3\) and any \(m\geq 0\), there are no nontrivial integral polynomials \[ p_0(n)=c_0+c_1n+\ldots+c_m n^m, p_1(n)=d_0+d_1n+\ldots+d_m n^m \] such that \[ p_0(n)a_{n+1}^{(r)}+p_1(n) a_n^{(r)}=0,n\geq 0, \] where \[ a_n^{(r)}=\sum_{k=0}^n \binom{n}{k}^r. \]
scientific article; zbMATH DE number 5880811