Definition:Bernoulli Numbers/Recurrence Relation

Definition
The Bernoulli numbers $B_n$ are a sequence of rational numbers defined by the recurrence relation:
 * $B_n = \begin{cases} 1 & : n = 0 \\ \displaystyle - \sum_{k \mathop = 0}^{n - 1} \binom n k \frac {B_k} {n - k + 1} & : n > 0 \end{cases}$

or equivalently:


 * $B_n = \begin{cases} 1 & : n = 0 \\ \displaystyle - \frac 1 {n+1} \sum_{k \mathop = 0}^{n - 1} \binom {n+1} k B_k & : n > 0 \end{cases}$

Also see

 * Equivalence of Definitions of Bernoulli Numbers