Unverified Commit e7637400 authored by ir1d's avatar ir1d Committed by GitHub
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Merge pull request #1263 from 24OI/TrisolarisHD-patch-1

Update catalan.md
parents d2419fd3 25b3661d
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该递推关系的解为:

$$
H_n=\frac{C_{2n}^{n}}{n+1}(n=1,2,3,\cdots)
H_n = \frac{\binom{2n}{n}}{n+1}(n \geq 2, n \in \mathbf{N_{+}})
$$

或者是
关于 Calalan 数的常见公式:

$$
H_n=H_0*H_(n-1)+H_1*H_(n-2)+...+H_(n-1)*H_0, (n>=2), H_0=H_1=1
H_n = \begin{cases}
    \sum_{i=1}^{n} H_{i-1} H_{n-i} & n \geq 2, n \in \mathbf{N_{+}}\\
    1 & n = 0, 1
\end{cases}
$$

或者是

$$
H_n=H_(n-1)*(4*n-2)/(n+1)
H_n = \frac{H_{n-1} (4n-2)}{n+1}
$$

或者是

$$
H_n=C_{2n}^{n}-C_{2n}^{n-1}
H_n = \binom{2n}{n} - \binom{2n}{n-1}
$$