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Combinatorics

Binomial coefficient

{c}
{title2=$T_{n,k}=\binom nk$}

= Pascal triangle
{c}
{synonym}

Row $n$ of Pascal's triangle consists of the <binomial coefficients> $\binom n0,\ldots,\binom nn$, beginning with row $0$. Boundary entries are one, and <Pascal's identity> says each interior entry is the sum of the two entries above it. The <hockey-stick identity> evaluates sums along its diagonals.


Pascal's triangle ( $T_{n, k} = (k n)$ )

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Pascal's triangle (Tn,k​=(kn​))