Generalized barred preferentisl arrangements

Abstract

We investigate a generalization of Fubini numbers. We present the combinatorial interpre- tation as barred preferential arrangements with some additional conditions on the blocks. We provide a proof for a generalization of Nelsen's Theorem. We consider these numbers from a probabilistic view point and demonstrate how they can be written in terms of the expectation of random descending factorial involving the negative binomial process.