What is Pascal's triangle?

Blaise Pascal published the workings of a triangular array showing the relationship between binary coefficients in said triangle. For instance:

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|.......................................1.........................................|

|..................................1........1....................................|

|..............................1.......2........1...............................|

|..........................1......3........3.......1...........................|

|......................1......4.......6.......4......1........................|

|...................1......5.....10....10......5......1...................|

|...............1......6.....15....20.....15.....6.....1...............|

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Each number in the above triangle is the sum of the two numbers right about it.

For example, 20 is the sum of 10 and 10, and 2 is the sum of 1 and 1.