[mooism2]

You've reinvented polynomials.

1

x + 1

x² + 2x + 1

x³ + 3x² + 3x + 1

...

You can think of Pascal's triangle as repeated multiplication by (x + 1).

[gokce]

hmmm, so every new digit is the coefficient of the next power?

(i.e. (x+1) = 1x^1 + 1x^0 => 1:1)

it makes sense, haven't thought about it..