The probability measure corresponding to 2-plane trees

Abstract

We study the probability measure ${\mu }_0$ for which the moment sequence is $\left(\genfrac{}{}{0ex}{}{3n}{n}\right)\frac{1}{n+1}$. We prove that ${\mu }_0$ is absolutely continuous, find the density function and prove that ${\mu }_0$ is infinitely divisible with respect to the additive free convolution.