What is the name of this table? I am looking for a name such as "Fibonacci sequence". I am assuming my table already has a name, but I guess it is possible that I invented it. Here is what it looks like: $$ \begin{array}{|l|l|l|l|l|l|l|} \hline 1 & 1 & 1 & 1 & 1 & 1 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 3 & 6 & 10 & 15 & 21 \\ \hline 1 & 4 & 10 & 20 & 35 & 56 \\ \hline 1 & 5 & 15 & 35 & 70 & 126 \\ \hline 1 & 6 & 21 & 56 & 126 & 252 \\ \hline \end{array} $$
Basically, the table is started by entering the number 1 in all the cells of the first column and the first row. Then, each cell is the sum of its up+left neighbor. So, cell (2,2) has value 2. Cell (2,3) has value 3. Etc.
UPDATE: The best answer so far is that it is basically Pascal's triangle but on a slant. I doubt there's a more specific name for it than that.
It is called a symmetric Pascal matrix.