Euler Zigzag Number
The number of Alternating Permutations for 
elements is sometimes called anEuler 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. SequenceA000111/M1492in ``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.
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