Definition:Euler Numbers/Sequence
Jump to navigation
Jump to search
Definition
The sequence of Euler numbers begins:
\(\ds E_0\) | \(=\) | \(\ds 1\) | ||||||||||||
\(\ds E_2\) | \(=\) | \(\ds -1\) | ||||||||||||
\(\ds E_4\) | \(=\) | \(\ds 5\) | ||||||||||||
\(\ds E_6\) | \(=\) | \(\ds -61\) | ||||||||||||
\(\ds E_8\) | \(=\) | \(\ds 1385\) | ||||||||||||
\(\ds E_{10}\) | \(=\) | \(\ds -50 \, 521\) | ||||||||||||
\(\ds E_{12}\) | \(=\) | \(\ds 2 \, 702 \, 765\) | ||||||||||||
\(\ds E_{14}\) | \(=\) | \(\ds -199 \, 360 \, 981\) | ||||||||||||
\(\ds E_{16}\) | \(=\) | \(\ds 19 \, 391 \, 512 \, 145\) | ||||||||||||
\(\ds E_{18}\) | \(=\) | \(\ds -2 \, 404 \, 879 \, 675 \, 441\) | ||||||||||||
\(\ds E_{20}\) | \(=\) | \(\ds 370 \, 371 \, 188 \, 237 \, 525\) | ||||||||||||
\(\ds E_{22}\) | \(=\) | \(\ds -69 \, 348 \, 874 \, 393 \, 137 \, 901\) | ||||||||||||
\(\ds E_{24}\) | \(=\) | \(\ds 15 \, 514 \, 534 \, 163 \, 557 \, 086 \, 905\) |
Odd index Euler numbers are all $0$.
This sequence is A122045 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Euler numbers
- Weisstein, Eric W. "Euler Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerNumber.html