1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
...

https://i.imgur.com/CeHuBvw.png

${}_n\mathrm{C}_r={}_n\mathrm{C}_{n-r}$ (좌우 대칭)

${}_{n+1}\mathrm{C}_r={}_n\mathrm{C}_{r-1}+{}_n\mathrm{C}_r$

----

[[이항정리,binomial_theorem]]에 의해
 (1 + x)^^n^^ = ,,n,,C,,0,, + ,,n,,C,,1,,x + ,,n,,C,,2,,x^^2^^ + … + ,,n,,C,,n,,x^^n^^
x = 1을 대입하면
 2^^n^^ = ,,n,,C,,0,, + ,,n,,C,,1,, + … + ,,n,,C,,n,,


[[수,number]]s들의 배열이며, 그 수는 [[이항계수,binomial_coefficient]] chk

----
확장/일반화 by Newton:
https://youtu.be/gMlf1ELvRzc?t=626

[[삼각형,triangle]]

----
Twins:
https://mathworld.wolfram.com/PascalsTriangle.html
http://rosettacode.org/wiki/Pascal%27s_triangle (PL 구현)
https://artofproblemsolving.com/wiki/index.php/Pascal%27s_triangle
http://oeis.org/wiki/Pascal_triangle
 그리고 (1,1)-Pascal triangle이 Pascal's triangle, (1,2)-Pascal triangle이 Lucas triangle, .... 일반화?
 [[https://oeis.org/wiki/(a,b)-Pascal_triangle]]