Special Counting Sequences
Chunwei Song · 2024
As a major component of the current monograph, Chapter 3 is devoted to inquiries of special counting sequences including the Catalan numbers, which caused the Catalan mania, refinements and more general versions such as the Narayana numbers, super Catalan numbers, Fuss-Catalan numbers, as well as the Schr¨oder numbers and their higher dimensional versions. Moreover, we discuss Stirling numbers of the first and second kinds, Bell numbers, Harmonic numbers, the integer partition numbers, as well as an introduction to the theory of Young tableaux with connections to combinatorial sequences.