Can someone tell me please how am I supposed to demonstrate the Worpitzky's identity :
$$ x^{n}=\sum_{k}\left\langle\begin{array}{l} n \\ k \end{array}\right\rangle\left(\begin{array}{c} x+k \\ n \end{array}\right) $$
2026-02-23 08:37:23.1771835843
Worpitzky's identity eulerian number - formula demonstration
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Exercise 6.14 in Concrete Mathematics suggests to use induction on $n$ and the following identity: $$x\binom{x+k}{n} = (k+1)\binom{x+k}{n+1} + (n-k)\binom{x+k+1}{n+1}$$