Manipulate[TraditionalForm[f[n]]->TraditionalForm@MomentConvert[f[n],g],{{f,Moment,"source"},{Moment,CentralMoment,FactorialMoment,Cumulant}},{{g,CentralMoment,"target"},{Moment,CentralMoment,FactorialMoment,Cumulant}},{{n,3},1,20,1}]