A000108 (OEIS entry for Catalan numbers)

The Catalan numbers, represented by OEIS A000108, are a sequence of natural numbers that appear in various counting problems in combinatorics. They quantify the number of ways to correctly match parentheses, the number of paths that do not cross a diagonal in a grid, and the arrangements of certain types of polygons, among other applications. The sequence begins with 1, 1, 2, 5, 14, and so forth. Catalan numbers have significance in mathematics, computer science, and even in algorithm design, illustrating the deep connections between different areas of study.