MMN-3842
Some identities for derangement numbers
Sibel Koparal; Nese Ömür; Kübra Nur Südemen;Abstract
In this paper, we give some identities involving derangement numbers. In addition, we derive nonlinear differential equation from the generating function of the derangement numbers and using this differential equation, obtain some identities including generalized harmonic numbers and derangement numbers. For example, for any positive integers N, n and r,
∑_{k=0}^{N}∑_{i=0}^{N-k}(-1)^{i}(r/k)((r+N-i-k)/(N-i-k))((d_{n-r+k}^{(r+N-i-k+1)})/(i!(n-r+k)!))=((D_{r}(n+N))/(n!N!)).
Vol. 23 (2022), No. 2, pp. 773-785