Rows in Pascal's Triangle containing Numbers in Arithmetic Sequence/Examples/1001, 2002, 3003

Example of Rows in Pascal's Triangle containing Numbers in Arithmetic Sequence
The integers:
 * $1001, 2002, 3003$

are in arithmetic sequence and appear in row $14$ of Pascal's triangle.

Proof
We have:

thus demonstrating the common difference of $1001$.

Then we have that row $14$ of Pascal's triangle is:
 * $1, 14, 91, 364, \color {red} {1001, 2002, 3003}, 3432, 3003, 2002, 1001, 364, 91, 14, 1$