A Stirling Encounter with Harmonic Numbers

A Generalization of Stirling Numbers

are called a weighted Stirling pair if f(g(x)) = g(f(x)) = x, i.e.,/and g are reciprocal. When W(x) = l, B^in.k) and B2(n,k) reduce to a Stirling type pair whose properties are exhibited in [7]. In this paper, we shall present a weighted Stirling pair that includes some previous generalizations of Stirling numbers as particular cases. Some related combinatorial and arithmetic properties are als...

Stirling Numbers and Generalized Zagreb Indices

We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.

Multi-Restrained Stirling Numbers

Given positive integers n, k, and m, the (n, k)-th mrestrained Stirling number of the first kind is the number of permutations of an n-set with k disjoint cycles of length ≤ m. Inverting the matrix consisting of the (n, k)-th m-restrained Stirling number of the first kind as the (n+1, k +1)-th entry, the (n, k)-th m-restrained Stirling number of the second kind is defined. In this paper, the mu...

Stirling Numbers and Records

The p-Stirling Numbers

The purpose of this article is to introduce p-Stirling numbers of the first and second kinds.