# Definition:Euler Numbers/Sequence

 $\displaystyle E_0$ $=$ $\displaystyle 1$ $\displaystyle E_2$ $=$ $\displaystyle -1$ $\displaystyle E_4$ $=$ $\displaystyle 5$ $\displaystyle E_6$ $=$ $\displaystyle -61$ $\displaystyle E_8$ $=$ $\displaystyle 1385$ $\displaystyle E_{10}$ $=$ $\displaystyle -50 \, 521$ $\displaystyle E_{12}$ $=$ $\displaystyle 2 \, 702 \, 765$ $\displaystyle E_{14}$ $=$ $\displaystyle -199 \, 360 \, 981$ $\displaystyle E_{16}$ $=$ $\displaystyle 19 \, 391 \, 512 \, 145$ $\displaystyle E_{18}$ $=$ $\displaystyle -2 \, 404 \, 879 \, 675 \, 441$ $\displaystyle E_{20}$ $=$ $\displaystyle 370 \, 371 \, 188 \, 237 \, 525$ $\displaystyle E_{22}$ $=$ $\displaystyle -69 \, 348 \, 874 \, 393 \, 137 \, 901$ $\displaystyle E_{24}$ $=$ $\displaystyle 15 \, 514 \, 534 \, 163 \, 557 \, 086 \, 905$
Odd index Euler numbers are all $0$.