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Pascal's triangle. It is named after the French mathematician, Blaise Pascal in much of the Western world, although other mathematicians studied it centuries before him in India, Greece, Iran, China, Germany, and Italy. The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top. The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. (Wikipedia)

The top of the triangle -

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

And you can continue on, using the same rules.

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