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$$\begin{aligned} & \boxed{ \begin{aligned} \textbf{暂无评定} &: \color{#ffffff}\colorbox{#bfbfbf}{\hspace{0.15cm}2\hspace{0.15cm}} \\ \textbf{入门} &: \color{#ffffff}\colorbox{#fe4c61}{\hspace{5cm}52\hspace{5cm}} \\ \textbf{普及-} &: \color{#ffffff}\colorbox{#f39c11}{\hspace{4.4cm}46\hspace{4.4cm}} \\ \textbf{普及/提高-} &: \color{#ffffff}\colorbox{#ffc116}{\hspace{1.3cm}14\hspace{1.3cm}} \\ \textbf{普及+/提高} &: \color{#ffffff}\colorbox{#52c41a}{\hspace{0.45cm}5\hspace{0.45cm}} \\ \textbf{提高+/省选-} &: \color{#ffffff}\colorbox{#3498db}{\hspace{0.45cm}5\hspace{0.45cm}} \\ \textbf{省选/NOI-} &: \color{#ffffff}\colorbox{#9d3dcf}{\hspace{0.05cm}1\hspace{0.05cm}} \\ \textbf{NOI/NOI+/CTSC} &: \color{#ffffff}\colorbox{#0e1d69}{\hspace{-0.05cm}0\hspace{-0.05cm}} \\ \end{aligned} } \\ & \hspace{4.5cm} \small{\textsf{\color{#52c41a}gf24131\color{b}的刷题记录（洛谷）}} \end{aligned}$$

$卡特兰数公式$

$$\begin{aligned} H(x)&=\frac{1- \sqrt{1-4x}}{2x}\\ &=\frac{1}{2x}\sum_{n\ge 1}\binom{2n-1}{n}\frac{1}{(2n-1)}2x^n\\ &=\sum_{n\ge 1}\binom{2n-1}{n}\frac{1}{(2n-1)}x^{n-1}\\ &=\sum_{n\ge 0}\binom{2n+1}{n+1}\frac{1}{(2n+1)}x^{n}\\ &=\sum_{n\ge 0}\binom{2n}{n}\frac{1}{n+1}x^{n}\\ \end{aligned}$$

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