\documentclass[12pt,a4paper,german]{article} \usepackage{url} %\usepackage{graphics} \usepackage{times} \usepackage[T1]{fontenc} \usepackage{ngerman} \usepackage{float} \usepackage{diagbox} \usepackage[utf8]{inputenc} \usepackage{geometry} \usepackage{amsfonts} \usepackage{amsmath} \usepackage{csquotes} \usepackage{graphicx} \usepackage{epsfig} \usepackage{paralist} \geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm} %%%%%%%%%% 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} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % DO NOT MODIFY THIS HEADER \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}