Distribution with many cumulants vanishing

Question

Let $X$ be a random variable. It is well-known that $X$ is normally distributed if and only if its last cumulants $\kappa_3 = \kappa_4 = ... = 0$ vanish. I was wondering if there are standard distributions satisfying $\kappa_m = ... = \kappa_n = 0$ for arbitrary $m<n\le\infty$, especially for $m=3$.