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

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

[[math]] M_k(\mu)=|P(k)| [[/math]]

then more generally find a measure [math]\mu_t[/math] whose moments are given by

[[math]] M_k(\mu_t)=\sum_{\pi\in P(k)}t^{|\pi|} [[/math]]

where [math]P(k)[/math] stands as usual for all partitions of [math]\{1,\ldots,k\}[/math].