卡特兰数的规律

卡特兰数的规律

$catalan(n)=\sum_{i=0}^{n-1}catalan(i)\times catalan(n-i-1)$

$catalan(n)=\frac{catalan(n-1)\times(4n-2)}{n+1}$

$catalan(n)=\frac{C_{2n}^n}{n+1}$

$catalan(n)=C_{2n}^n-C_{2n}^{n-1}$

$catalan(n)=\frac{\sum_{i=0}^{n}(C_n^i)^2}{n+1}$

$catalan(n)=\frac{(2n)!}{(n+1)!n!}$

$如果n=2^k-1,则catalan(n)\equiv1(mod\ 2)\\ 其余情况catalan(n)\equiv0(mod\ 2)$

来源：CSDN

作者：冷酷|射手

链接：https://blog.csdn.net/fangfengwei/article/details/104132678