In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written . It is the coefficient of the x ^k term in the polynomial expansion of the binomial power (1 + x) ⁿ. Under suitable circumstances the value of the coefficient is given by the expression . 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.