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  1. R

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

    I have derived an explicit formula for the" [Broken], 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...
  2. R

    Solving non-homogeneous differential equation with variable coefficients

    Here is a paper written by me:" [Broken] Basically, it uses operator method to solve linear non-homogeneous ordinary differential equation with variable...