Binomial coefficient

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written ${\displaystyle {\tbinom {n}{k}}}$. It is the coefficient of the x^k term in the polynomial expansion of the binomial power (1 + x)ⁿ. The value of the coefficient is given by the expression ${\displaystyle {\tfrac {n!}{k!(n-k)!}}}$. Arranging binomial coefficients into rows for successive values of n, and in which k ranges from 0 to n, gives a triangular array called Pascal's triangle.

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