Bernoulli number

Remarks

The first values are $B_0 = 1$, $B_1 = -\frac{1}{2}$, $B_2 = \frac{1}{6}$, $B_4 = -\frac{1}{30}$ and $B_6 = \frac{1}{42}$. Also $B_n = 0$ for each odd $n \ge 3$. Some authors use the convention $B_1 = +\frac{1}{2}$, from the series $\frac{t e^t}{e^t - 1}$. They appear in the formulas for the sums of powers $1^k + 2^k + \dots + n^k$, and in the values $\zeta(2n)$ of the Riemann zeta function. They are named after Jacob Bernoulli. Seki Takakazu tabulated them in his Katsuyō Sanpō of 1712.