Catalan number
= Catalan number
{c}
{title2=$C_n$}
{wiki}
The Catalan number
$$
C_n=\frac1{n+1}\binom{2n}{n}
$$
counts <Dyck paths> of semilength $n$. Its ordinary generating function $C(x)=\sum_{n\geq0}C_nx^n$ satisfies $C(x)=1+xC(x)^2$.
= Catalan number
{c}
{title2=$C_n$}
{wiki}
The Catalan number
$$
C_n=\frac1{n+1}\binom{2n}{n}
$$
counts <Dyck paths> of semilength $n$. Its ordinary generating function $C(x)=\sum_{n\geq0}C_nx^n$ satisfies $C(x)=1+xC(x)^2$.