Hexagonal numbers

Hexagonal numbers are figurate numbers (numbers that can be represented by a regular geometric arrangement of equally spaced points), and 6-polygonal numbers of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... . Every hexagonal number is also a triangular number.
Like the triangular numbers, the hexagonal numbers are found in the third diagonal of Pascal's triangle:

             1            Row 0

            1 1           Row 1

           1 2 1          Row 2 

          1 3 3 1         Row 3 

         1 4 6 4 1        Row 4 

       1 5 10 10 5 1      Row 5

     1 6 15 20 15 6 1     Row 6

    1 7 21 35 35 21 7 1   Row 7

   1 8 28 56 70 56 28 8 1 Row 8