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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
\def \name {Valentin Brandl}					%
\def \matrikel {108018274494}				%
\def \pname {Marvin Herrmann}				%
\def \pmatrikel {108018265436}				%
\def \gruppe {2 (Mi 10-12 Andre)}
\def \uebung {2}								%
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\newcommand{\hwsol}{
\vspace*{-2cm}
\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
\noindent \pmatrikel \quad \pname \\
\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
}

\begin{document}
%Import header
\hwsol

\section*{Aufgabe 2.2}
\begin{enumerate}[1.]

	\item Zyklenzerlegung: $(1\ 2\ 4) (3) (5\ 9) (6) (7\ 8)$

		2 Fixpunkte: $3$ und $6$

	\item
		\begin{tabular}{c|cccccccccc}
			$n / k$ & 0&1&2&3&4&5&6&7&8&9 \\\hline
			0 & 1 &&&&&&&&& \\
			1 & 0 & 1 &&&&&&&& \\
			2 & 0 & 1 &1&&&&&&& \\
			3 & 0 & 2 & 3 & 1 &  &  &  &  &  &  \\
			4 & 0 & 6 & 11 & 6 & 1 &  &  &  &  &  \\
			5 & 0 & 24 & 50 & 35 & 10 & 1 &  &  &  &  \\
			6 & 0 & 120 & 274 & 225 & 85 & 15 & 1 &  &  &  \\
			7 & 0 & 720 & 1764 & 1624 & 735 & 175 & 21 & 1 &  &  \\
			8 & 0 & 5040 & 13068 & 13132 & 6769 & 1960 & 322 & 28 & 1 &  \\
			9 & 0 & 40320 & 109584 & 118124 & 67284 & \underline{22449} & 4536 & 546 & 36 & 1 \\
		\end{tabular}

		\begin{eqnarray*}
			s_{n.k} &=& s_{n-1,k-1} + (n-1)s_{n-1,k} \text{ mit} \\
			s_{0,0} &=& 1 \\
			s_{n,0} &=& 0 \\
			s_{n,n} &=& 1 \\\\
			s_{9,5} &=& 22449
		\end{eqnarray*}

\end{enumerate}

\end{document}

