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
See also Alternating Permutation, Entringer Number, Secant Number, Tangent Number
References
Ruskey, F. ``Information of Alternating Permutations.''
http://sue.csc.uvic.ca/~cos/inf/perm/Alternating.html.
Sloane, N. J. A. Sequence
A000111/M1492
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.