Output the Euler Numbers Given a non-negative integer \$n ,\$ output the \$n^{\text{th}}\$ Euler number (OEIS A122045).
All odd-indexed Euler numbers are \$0 .\$ The even-indexed Euler numbers can be computed with the following formula (\$i \equiv \sqrt{-1}\$ refers to the imaginary unit):
$$
E_{2n}
= i
\sum_{k=1}^{2n+1}{
  \sum_{j=0}^{k}{
    \left(\begin{array}{c}k \\ j \end{array}\right)
    \frac{{\left(-1\right)}^{j} {\left(k-2j\right)}^{2n+1}}{2^k i^k k}
  }
}
\,.
$$
Rules

\$n\$ will be a non-negative integer such that the \$n^{\text{th}}\$ Euler number is within the representable range of integers for your language.

Test Cases
0 -&gt; 1
1 -&gt; 0
2 -&gt; -1
3 -&gt; 0
6 -&gt; -61
10 -&gt; -50521
20 -&gt; 370371188237525
Mathematica, 6 bytes

EulerE


-cough-