Reading on wikipedia's page about Gamma function I've read this interesting formula:
$$\Gamma^{(n)}(1)=(-1)^nn!\sum_{\pi \vdash n}\prod_{i=1}^r\frac {\zeta^*(a_i)}{k_i!a_i}$$
But I don't fully understand it: I know what the Zeta with the "$*$" means but I don't know what the symbol "$\vdash$" stands for...
Next Wikipedia says that $\pi=(a_1,\dots,a_1,\dots,a_r,\dots,a_r)$ where every $a_i$ is taken $k_i$ times but I don't know what partitions are and I don't get how $a_i$ and $k_i$ comes from...
Can someone please explain me what technique this formula uses and maybe do some examples on how to calculate the first terms ? Is there any other ways to write this relation that don't deal with partitions and so on?