New posts in Catalan Numbers

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

Catalan numbers formula derivation

Catalan's constant and $\int_{0}^{2 \pi} \int_{0}^{2 \pi} \ln(\cos^{2} \theta + \cos^{2} \phi) ~d \theta~ d \phi$

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

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}$

Generating series of Catalan numbers

Identity with Catalan numbers

How many arrangements of the digits 1,2,3, ... ,9 have this property?

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

Simplifying Catalan number recurrence relation