Faulhaber's formula
Expression for sums of powers / From Wikipedia, the free encyclopedia
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In mathematics, Faulhaber's formula, named after the early 17th century mathematician Johann Faulhaber, expresses the sum of the p-th powers of the first n positive integers
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as a polynomial in n. In modern notation, Faulhaber's formula is
Here, is the binomial coefficient "p + 1 choose r", and the Bj are the Bernoulli numbers with the convention that .