The number of partitions of an n element set is given by the nth Bell number. If the elements in the block are ordered, we get the L n numbers – the horizontal sums of the Lah numbers. If, in turn, the order of the blocks is taken into account, we arrive at another counting sequence: that of the Fubini numbers. In this chapter we study this sequence; it will turn out that it is connected also to some interesting counting problems regarding permutations.