eulerfrac

Function: eulerfrac
Section: combinatorics
C-Name: eulerfrac
Prototype: L
Help: eulerfrac(n): Euler number E_n, as a rational number.
Doc: Euler number\sidx{Euler numbers} $E_n$,
 where $E_0=1$, $E_1=0$, $E_2=-1$, \dots, are integers such that
 $$ \dfrac{1}{\cosh t} = \sum_{n\geq 0} \dfrac{E_n}{n!} t^n. $$
 The argument $n$ should be a nonnegative integer.
 \bprog
 ? vector(10,i,eulerfrac(i))
 %1 = [0, -1, 0, 5, 0, -61, 0, 1385, 0, -50521]
 ? eulerfrac(20000);
 ? sizedigit(%))
 %3 = 73416
 @eprog