Graf's book on hyperfunction theory says (page $36$) that
$$\frac1{(x-i0)^n}=\frac{(-1)^{n-1}\pi i}{(n-1)!}\delta^{(n-1)}(x)+\operatorname{fp}\frac1{x^n},$$
while the table of Fourier transforms says that the Fourier transform of $x^n$ is $2\pi i^n\delta^{(n)}(x)$.
The apparent contradiction is in the factorial factor $n!$ Based on the second formula the first one should be
$$\frac1{(x-i0)^n}=(-1)^{n-1}n\pi i\delta^{(n-1)}(x)+\operatorname{fp}\frac1{x^n}$$
Where is the mistake?