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

$A_n = i^{n+1}\sum _{k=1}^{n+1} \sum _{j=0}^k {k\choose{j}} \frac{(-1)^j(k-2j)^{n+1}}{2^ki^kk}$

For details, please refer to my article in Voofie:

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

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? Also, if possible, can anyone provide some reference to other explicit formula for $A_n$?

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

$$A_n = i^{n+1}\sum _{k=1}^{n+1} \sum _{j=0}^k {k\choose{j}} \frac{(-1)^j(k-2j)^{n+1}}{2^ki^kk}$$

For details, please refer to my article in Voofie:

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

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? Also, if possible, can anyone provide some reference to other explicit formula for $A_n$?

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

$A_n = i^{n+1}\sum _{k=1}^{n+1} \sum _{j=0}^k {k\choose{j}} \frac{(-1)^j(k-2j)^{n+1}}{2^ki^kk}$

For details, please refer to my article in Voofie:

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

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?

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

$A_n = i^{n+1}\sum _{k=1}^{n+1} \sum _{j=0}^k {k\choose{j}} \frac{(-1)^j(k-2j)^{n+1}}{2^ki^kk}$

For details, please refer to my article in Voofie:

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

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? Also, if possible, can anyone provide some reference to other explicit formula for $A_n$?

I have derived an explicit formula for the Euler zigzag numbers, 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:

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

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?

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

$A_n = i^{n+1}\sum _{k=1}^{n+1} \sum _{j=0}^k {k\choose{j}} \frac{(-1)^j(k-2j)^{n+1}}{2^ki^kk}$

For details, please refer to my article in Voofie:

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

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?