Combinatorics, Pascal's Triangle
is best known for his triangle of numbers, with 1 at the apex.
The jth row (descending) contains j numbers,
centered about a vertical line that passes through the apex.
Thus each number has two numbers below it,
one slightly to the left and one slightly to the right.
The second row, just below the apex,
has two 1's
just to the left and right of the midline.
The third row contains 1,2,1, with 2 on the midline.
Each number in the triangle is the sum of the two numbers from above.
Boundary numbers are always 1.
Here are the first 8 rows of Pascal's triangle.