Central binomial coefficient

Remarks

The first values, for $n = 0, 1, 2, 3, 4$, are $1, 2, 6, 20, 70$. It is the middle entry of row $2n$ of Pascal's triangle, and the largest entry of that row. It counts the lattice paths from $(0, 0)$ to $(n, n)$ with unit steps right and up. The closed formula for Catalan numbers divides it by $n + 1$.