Exponential generating function
= Exponential generating function
{title2=$A(z)=\sum_{n\geq0}a_nz^n/n!$}
An exponential <generating function> encodes a <sequence> using the displayed <factorial> denominators. It is especially useful for counting labelled combinatorial structures: taking an unordered set of structures with positive size corresponds to exponentiating their exponential generating function. The <rooted-tree generating function> illustrates this through $T=z e^T$.