Does anyone know a reference for the solution of the generalized derangement problem via Laguerre polynomials? The Wikipedia article here says that this is an application of inclusion-exclusion, but I don't see how.
This formula was used by joriki in a nice MSE answer here.
The article below solves the generalized derangement problem with inclusion-exclusion, but without Laguerre polynomials.
Reference: Finn F. Knudsen and Ivar Skau, "On the Asymptotic Solution of a Card-Matching Problem", Mathematics Magazine 69 (1996), 190-197.