An Euler zigzag number alternating
permutations of inequalities A000111 ). For a nonnegative
integer
(1)
where Entringer number . For permutations . For permutations
of
The Entringer numbers satisfy
(2)
and the recurrence relation
(3)
for
See also Alternating Permutation ,
Entringer Number ,
Secant
Number ,
Tangent Number
Explore with Wolfram|Alpha
References Ruskey, F. "Information of Alternating Permutations." https://web.archive.org/web/20170424224013/http://theory.cs.uvic.ca/inf/perm/Alternating.html . Sloane,
N. J. A. Sequence A000111 /M1492
in "The On-Line Encyclopedia of Integer Sequences." Referenced
on Wolfram|Alpha Euler Zigzag Number
Cite this as:
Weisstein, Eric W. "Euler Zigzag Number."
From MathWorld https://mathworld.wolfram.com/EulerZigzagNumber.html
Subject classifications
counts the down-up alternating
permutations of 
objects, with inequalities 
and the convention 
. The initial values are 1, 1, 1, 2, 5, 16, 61, ... (OEIS
A000111). For a nonnegative
integer 
,
is an Entringer number. For 
, including both starting orientations gives 
permutations. For 
, the number of permutations
of 
elements that start with 
and then alternate down and up is 
for 
.
.
