\begin{tabular}{*{22}{|c}|}
       \hline \backslashbox{$n$}{$k$}  & \cellcolor{Moccasin}0 & \cellcolor{Moccasin}1 & \cellcolor{Moccasin}2 & \cellcolor{Moccasin}3 & \cellcolor{Moccasin}4 & \cellcolor{Moccasin}5 & \cellcolor{Moccasin}6 & \cellcolor{Moccasin}7 & \cellcolor{Moccasin}8 & \cellcolor{Moccasin}9 & \cellcolor{Moccasin}10 & \cellcolor{Moccasin}11 & \cellcolor{Moccasin}12 & \cellcolor{Moccasin}13 & \cellcolor{Moccasin}14 & \cellcolor{Moccasin}15 & \cellcolor{Moccasin}16 & \cellcolor{Moccasin}17 & \cellcolor{Moccasin}18 & \cellcolor{Moccasin}19 & \cellcolor{Moccasin}20\\\hline\cellcolor{Moccasin}1&1&1&&&&&&&&&&&&&&&&&&&\\\hline\cellcolor{Moccasin}2&1&2&1&&&&&&&&&&&&&&&&&&\\\hline\cellcolor{Moccasin}3&1&3&3&1&&&&&&&&&&&&&&&&&\\\hline\cellcolor{Moccasin}4&1&4&6&4&1&&&&&&&&&&&&&&&&\\\hline\cellcolor{Moccasin}5&1&5&10&10&5&1&&&&&&&&&&&&&&&\\\hline\cellcolor{Moccasin}6&1&6&15&20&15&6&1&&&&&&&&&&&&&&\\\hline\cellcolor{Moccasin}7&1&7&21&35&35&21&7&1&&&&&&&&&&&&&\\\hline\cellcolor{Moccasin}8&1&8&28&56&70&56&28&8&1&&&&&&&&&&&&\\\hline\cellcolor{Moccasin}9&1&9&36&84&126&126&84&36&9&1&&&&&&&&&&&\\\hline\cellcolor{Moccasin}10&1&10&45&120&210&252&210&120&45&10&1&&&&&&&&&&\\\hline\cellcolor{Moccasin}11&1&11&55&165&330&462&462&330&165&55&11&1&&&&&&&&&\\\hline\cellcolor{Moccasin}12&1&12&66&220&495&792&924&792&495&220&66&12&1&&&&&&&&\\\hline\cellcolor{Moccasin}13&1&13&78&286&715&1287&1716&1716&1287&715&286&78&13&1&&&&&&&\\\hline\cellcolor{Moccasin}14&1&14&91&364&1001&2002&3003&3432&3003&2002&1001&364&91&14&1&&&&&&\\\hline\cellcolor{Moccasin}15&1&15&105&455&1365&3003&5005&6435&6435&5005&3003&1365&455&105&15&1&&&&&\\\hline\cellcolor{Moccasin}16&1&16&120&560&1820&4368&8008&11440&12870&11440&8008&4368&1820&560&120&16&1&&&&\\\hline\cellcolor{Moccasin}17&1&17&136&680&2380&6188&12376&19448&24310&24310&19448&12376&6188&2380&680&136&17&1&&&\\\hline\cellcolor{Moccasin}18&1&18&153&816&3060&8568&18564&31824&43758&48620&43758&31824&18564&8568&3060&816&153&18&1&&\\\hline\cellcolor{Moccasin}19&1&19&171&969&3876&11628&27132&50388&75582&92378&92378&75582&50388&27132&11628&3876&969&171&19&1&\\\hline\cellcolor{Moccasin}20&1&20&190&1140&4845&15504&38760&77520&125970&167960&184756&167960&125970&77520&38760&15504&4845&1140&190&20&1\\\hline\end{tabular}