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In mathematics, Pascal's rule is a combinatorial identity about binomial coefficients. It states that for positive natural numbers n and k,
where {\displaystyle {\tbinom {n}{k}}} is a binomial coefficient; one interpretation of which is the coefficient of the x term in the expansion of. There is no restriction on the relative sizes of n and k, since, if n < k the value of the binomial coefficient is zero and the identity remains valid.
Pascal's rule can also be viewed as a statement that the formula
solves the linear two-dimensional difference equation
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