ThmDex – An index of mathematical definitions, results, and conjectures.

Alternative basic real arithmetic expressions for Catalan sequence

Formulation 0

Let $C : \mathbb{N} \to \mathbb{N}$ be the D4139: Catalan sequence.

Then

(i)	\begin{equation} n C_n = \binom{2 n}{n + 1} \end{equation}
(ii)	\begin{equation} C_n = \binom{2 n}{n} - \binom{2 n}{n + 1} \end{equation}