The Cartan's triangle (no Wikipedia article), is the Pascal's triangle's OLDER BROTHER, so to speak. The number on the left is doubled everytime, while the Pascal's triangle is not. The numbers in the Cartan's triangle are related with hypercubes.
The First 10 Rows edit
1
2 1
4 4 1
8 12 6 1
16 32 24 8 1
32 80 80 40 10 1
64 192 240 160 60 12 1
128 448 672 560 280 84 14 1
256 1024 1792 1792 1120 448 112 16 1
512 2304 4608 5376 4032 2016 672 144 18 1
The Cartan's triangle.
As you see, these are powers of 21 (12 if made backwards), because as you see in Row 1, there is 21. And in the second row, you see 441 which is 21². As you go on, you see two+ digit numbers on the Cartan's triangle. So then you do the same thing to it; carry it down to the number on the left. Here's a link on the Cartan's triangle: Cartan's triangle
- Note: If you have Excel, you will be able to make the Cartan's triangle bigger and bigger.
Here is OEIS on Cartan's Triangle