Function: bernfrac
Section: combinatorics
C-Name: bernfrac
Prototype: L
Help: bernfrac(n): Bernoulli number B_n, as a rational number.
Doc: Bernoulli number\sidx{Bernoulli numbers} $B_{n}$,
 where $B_{0}=1$, $B_{1}=-1/2$, $B_{2}=1/6$,\dots, expressed as a rational
 number.
 The argument $n$ should be a nonnegative integer. The function \tet{bernvec}
 creates a cache of successive Bernoulli numbers which greatly speeds up
 later calls to \kbd{bernfrac}:
 \bprog
 ? bernfrac(20000);
 time = 107 ms.
 ? bernvec(10000); \\ cache B_0, B_2, ..., B_20000
 time = 35,957 ms.
 ? bernfrac(20000); \\ now instantaneous
 ?
 @eprog
