New posts in catalan-numbers

An identity involving Catalan numbers and binomial coefficients.

Catalan numbers: bijection between applications of a binary operator and Dyck words.

How to deal with this double summation?

Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths

Prove a combinatorial identity: $ \sum_{n_1+\dots+n_m=n} \prod_{i=1}^m \frac{1}{n_i}\binom{2n_i}{n_i-1}=\frac{m}{n}\binom{2n}{n-m}$

Number of ways to pair off $2n$ points such that no chords intersect

Identity with Catalan numbers

Finding relatives of the series $\varphi =\frac{3}{2}+\sum_{k=0}^{\infty}(-1)^{k}\frac{(2k)!}{(k+1)!k!2^{4k+3}}$.

Cashier has no change... catalan numbers.. probability question

Generating function of $f(n) = C_n - \sum_{k=1}^{n-1}\binom{n}{k}f(n-k)$

Using the Catalan numbers

Closed form for $ S(m) = \sum_{n=1}^\infty \frac{2^n \cdot n^m}{\binom{2n}n} $ for integer $m$?

How do the Catalan numbers turn up here?

Simplifying Catalan number recurrence relation