Walter de Gruyter
We provide combinatorial proofs of identities published by Alzer and Prodinger. These identities include that for integers b, n, and r with b ≥ 1 and n − 1 ≥ r ≥ 0 we have
and for integers b, n, and r with b ≥ 0 and n − 1 ≥ r ≥ 0 we have
Our combinatorial proofs generalize squares to sth powers, and involve generalized Eulerian numbers and generalized Delannoy numbers.
Engbers, John and Stocker, Christopher, "Combinatorial Proofs of Identities of Alzer and Prodinger and Some Generalizations" (2018). Mathematics, Statistics and Computer Science Faculty Research and Publications. 586.