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diff --git a/content/math/math.tex b/content/math/math.tex index 1bcf85d..97b6a24 100644 --- a/content/math/math.tex +++ b/content/math/math.tex @@ -438,7 +438,7 @@ $1,~1,~2,~5,~14,~42,~132,~429,~1430,~4862,~16796,~58786,~208012,~742900$ \item Anzahl an Klammerausdrücken mit $n+k$ Klammerpaaren, die mit $\texttt{(}^k$ beginnen. \end{itemize} \[C^k_0 = 1\qquad C^k_n = \sum\limits_{\mathclap{a_0+a_1+\dots+a_k=n}} C_{a_0}C_{a_1}\cdots C_{a_k} = -\frac{k+1}{n+k+1}\binom{2n+k}{n} = \frac{(2n+k-1)(2n+k)}{n(n+k+1)} C_{n-1}\] +\frac{k+1}{n+k+1}\binom{2n+k}{n} = \frac{(2n+k-1)(2n+k)}{n(n+k+1)} \cdot C^k_{n-1}\] \paragraph{\textsc{Euler}-Zahlen:} $|~1~|~1~|~1,~1~|~1,~4,~1~|~1,~11,~11,~1~|~1,~26,~66,~26,~1~|$ |