Enumerating Some Stable Partitions Involving Stirling and r-Stirling Numbers of the Second Kind

Fubini Numbers and Polynomials of Graphs

“…These numbers already appeared before in the literature in connection with graph colourings, but the above-mentioned authors were the first who considered them from an enumerative point of view, as generalizations of classical Stirling and Bell numbers. A detailed study was given in [21], and several recent results can be found in [1][2][3]16,18,20,22]. One can define the corresponding Bell poly-…”

Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach

“…The fourth is well known and can be found in Comtet [2,Chap. 5] (see also Belbachir et al [15] for a generalization of this formula to r-Stirling numbers of the second kind). The last one is used in many occasions to define the Stirling numbers of the second kind (see, for instance, Abramowitz and Stegun [1, p. 824]).…”