Abstract
There have been many studies of Bernoulli numbers since Jakob Bernoulli first used the numbers to compute sums of powers, 1 p + 2 p + 3 p + ··· + np , where n is any natural number and p is any non-negative integer. By examining patterns of these sums for the first few powers and the relation between their coefficients and Bernoulli numbers, the author hypothesizes and proves a new recursive algorithm for computing Bernoulli numbers, sums of powers, as well as m-ford sums of powers, which enrich the existing literatures of Bernoulli numbers.
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