Asymptotic Formula for Bernoulli Numbers

Theorem
The even Bernoulli numbers can be approximated by the asymptotic formula:


 * $\displaystyle B_{2 n} \sim \left({- 1}\right)^{n + 1} 4 \sqrt{ \pi n} \left({\frac n {\pi e}}\right)^{2 n}$

where $B_n$ denotes the $n$th Bernoulli number and $\sim$ denotes asymptotically equal.