I have derived an explicit formula for the [Euler zigzag numbers][1], the number of alternating permutations for n elements:

$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} $

For details, please refer to my article in [Voofie][2]:

[An Explicit Formula for the Euler zigzag numbers (Up/down numbers) from power series][3]

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?


  [1]: http://mathworld.wolfram.com/EulerZigzagNumber.html
  [2]: http://www.voofie.com/
  [3]: http://www.voofie.com/content/117/an-explicit-formula-for-the-euler-zigzag-numbers-updown-numbers-from-power-series/