Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence (Q1040207)

Given a sequence \(a_n\), the Euler-Seidel matrix of this sequence is defined recursively as \(a_n^0=a_n\) for \(n\geq 0\), and \(a_n^k=a_n^{k-1}+a_{n+1}^{k-1}\) for \(n\geq 0, k\geq 1\). The paper studies \(r\)-Stirling numbers and hyperharmonic numbers in the context of Euler-Seidel matrices and expresses the exponential generating function of hyperharmonic numbers in terms of hypergeometric functions.