组合数学少不了二项式，今天来补一补。
0 |1 |2 | 3 |4 |5 |6 |7 |8
0 1 | | | | | | | |
1 1 |1 | | | | | | |
2 1 |2 |1 | | | | | |
3 1 |3 |3 |1 | | | | |
4 1 |4 |6 |4 |1 | | | |
5 1 |5 |10 |10 | 5 |1 | | |
6 1 |6 |15 |20 |15 |6 |1 | |
7 1 |7 |21 |35 |35 |21 |7 |1 |
8 1 |8 |28 |56 |70 |56 |28 |8 | 1
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例：
C(8,3)=56=C(7,3)+C(7,2)
可推：C（n,i)=C(n-1,i)+C(n-1,i-1)
k=2列为四面体数。
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二项式定理：
（x+y)^n=x^n + C(n,1)(x^n-1) *y + C(n,2)(x^n-2 )*(y^2) + ...... + C(n,n-1)x *(y^n-1) + y^n