We provide a concise combinatorial proof for the solution of the general two-term recurrence \(u(n, k) = u(n-1, k-1) + (a_{n-1}+b_{k})u(n-1, k)\), initially discovered by Mansour et al. \([4]\).
Citation
Sabrina X.M.Pang, Lun Lv. A Combinatorial Proof of a General Two-Term Recurrence[J], Ars Combinatoria, Volume 118. 429-431. .