Catalan

\[1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900,... \]

\[f(n)= \sum\limits_{i=0}^{n-1} f(i) \times f(n-i-1) \]

\[f(n)=\dfrac{f(n-1) \times (4 \times n -2) }{n+1} \]

\[f(n)=\dfrac{C_{2n}^{n}}{n+1} \]

\[f(n)=C_{2n}^{n} - C_{2n}^{n-1} \]