Bernoulli numbers are a sequence of rational numbers that are important in number theory and mathematical analysis. They are defined using a specific formula involving the Riemann zeta function and can be generated through the expansion of the function \fracxe^x - 1 . These numbers appear in various mathematical contexts, such as in the calculation of sums of powers of integers and in the Euler-Maclaurin formula. The first few Bernoulli numbers are B_0 = 1 , B_1 = -\frac12 , B_2 = \frac16 , and B_3 = 0 .