I have derived an explicit formula for the http://mathworld.wolfram.com/EulerZigzagNumber.html" [Broken], the number of alternating permutations for n elements:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] A_j=i^{j+1}\sum _{n=1}^{j+1} \sum _{k=0}^n \frac{C_k^n(n-2k)^{j+1}(-1)^k}{2^ni^nn} [/tex]

For details, please refer to my article in http://www.voofie.com" [Broken]:

http://www.voofie.com/content/117/an-explicit-formula-for-the-euler-zigzag-numbers-updown-numbers-from-power-series/" [Broken]

I would like to ask, if my formula is new, or is it a well known result? Since I can't find it in Wikipedia or MathWorld. If it is an old formula, can anyone give me some reference to it?

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# Explicit formula for Euler zigzag numbers(Up/down numbers)

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