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Euler Zigzag Number

The number of alternating permutations for n elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on n elements for which the first element is k by E(n,k). Then E(1,1)=1 and

E(n,k)={0 for k>=n or k<1; E(n,k-1)+E(n-1,n-k) otherwise.
(1)

where E(n,k) is an Entringer number.

See also

Alternating Permutation, Entringer Number, Secant Number, Tangent Number

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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."

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Euler Zigzag Number

Cite this as:

Weisstein, Eric W. "Euler Zigzag Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EulerZigzagNumber.html

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