Catalan数

通项

$f(n)=C(2n,n)/(n+1)$

递推

$f(n)=f(n-1)*2(2n-1)/(n+1)$

$f(n)=C(2n,n)-C(2n,n+1)$

其前几项为（从第零项开始） :

$1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452 ...$