\begin{definition}[Definition:Euler Numbers/Sequence]
The sequence of Euler numbers begins:
{{begin-eqn}}
{{eqn | l = E_0
      | r = 1
      | c = 
}}
{{eqn | l = E_2
      | r = -1
      | c = 
}}
{{eqn | l = E_4
      | r = 5
      | c = 
}}
{{eqn | l = E_6
      | r = -61
      | c = 
}}
{{eqn | l = E_8
      | r = 1385
      | c = 
}}
{{eqn | l = E_{10}
      | r = -50 \, 521
      | c = 
}}
{{eqn | l = E_{12}
      | r = 2 \, 702 \, 765
      | c = 
}}
{{eqn | l = E_{14}
      | r = -199 \, 360 \, 981
      | c = 
}}
{{eqn | l = E_{16}
      | r = 19 \, 391 \, 512 \, 145
      | c = 
}}
{{eqn | l = E_{18}
      | r = -2 \, 404 \, 879 \, 675 \, 441
      | c = 
}}
{{eqn | l = E_{20}
      | r = 370 \, 371 \, 188 \, 237 \, 525
      | c = 
}}
{{eqn | l = E_{22}
      | r = -69 \, 348 \, 874 \, 393 \, 137 \, 901
      | c = 
}}
{{eqn | l = E_{24}
      | r = 15 \, 514 \, 534 \, 163 \, 557 \, 086 \, 905
      | c = 
}}
{{end-eqn}}
Odd index Euler numbers are all $0$.
{{OEIS|A122045}}
\end{definition}