binomial coefficient

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The coefficient of a power of x in the binomial expansion of (1+x)n. The general binomial coefficient is defined, for any value of n and for any positive integer r, by . By convention, . Suppose now that n is a non-negative integer. In this case is an integer and . Furthermore,. If rn then is also written as nCr (see combination) and . The phrase ‘binomial coefficient’ appears in English in a mathematics text of 1876.

Subjects: Mathematics.

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