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Pascal's triangle. Newton's binomial

Pascal’s triangle
On the nn-th “horizontal” row (counting the apex as n=0n=0) stand Cn0,Cn1,,CnnC_n^0,\,C_n^1,\,\ldots,\,C_n^n. Pascal’s rule Cnk=Cn1k1+Cn1kC_n^k=C_{n-1}^{k-1}+C_{n-1}^k builds the triangle: each interior entry is the sum of the two numbers above it. Row sum: k=0nCnk=2n\sum_{k=0}^n C_n^k=2^n — the number of all subsets of an nn-element set.
Boundary 11s on the left and right — Cn0=Cnn=1C_n^0=C_n^n=1
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