New posts in Catalan Numbers

Finding the the number of Lattice paths with three steps.

Let $n ≥ 3$. Find the number of NE lattice paths from $(0, 0)$ to $(n, n)$ that touch the diagonal $y = x$ at least twice

Generalizing Catalan numbers: number of ways where we cross the diagonal $k$ times.

Prove: $\sum\limits_{k=0}^{n}\frac{1}{k+1}\binom{2k}{k}\binom{2n-2k}{n-k} = \binom{2n+1}{n}$

Bijection between Dyck paths with $k$ peaks and $n+1-k$ peaks

Generating function of a parametrized binomial coefficient

Putting socks and shoes on a spider

Catalan numbers and triangulations

Asymptotic approximation of Catalan Numbers

Number of Dyck Paths that touch the diagonal exactly $k$ times?