The number of alternating permutations for elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on elements for which the first element is by . Then and
(1)
|
where is an Entringer number.
The number of alternating permutations for elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on elements for which the first element is by . Then and
(1)
|
where is an Entringer number.
Weisstein, Eric W. "Euler Zigzag Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerZigzagNumber.html