[math] \newcommand{\mathds}{\mathbb}[/math]

Find a probability measure [math]\nu[/math] whose moments are given by

[[math]] M_k(\nu)=|NC_2(k)| [[/math]]

then find as well a probability measure [math]\eta[/math] whose moments are given by

[[math]] M_k(\eta)=|NC(k)| [[/math]]

where [math]NC[/math] stands for “noncrossing”. Then try as well the parametric case.