## Euler Zigzag 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

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.