For example to get from the generating series $G(t)$ of a connected species to the generating series of the set of its structures $G^*(t) F(t)$ the formula is $$G^*(t) F(t) = \exp(G^*(t)) exp(G(t)) = 1 + \dots .$$ .. $. This '$1$'$1$at degree zero is the empty structure. 2 fix markup The empty structure is ''disconnected'' and the definition of a tree is ''connected acyclic graph''. For example to get from the generating series$G(t)$of a connected species to the generating series of the set of its structures$ G^(t) G^*(t) $the formula is $$G^(t) G^*(t) = \exp(G^*(t)) = 1 + \dots ...$$. This'$1$$This '1' at degree zero is the empty structure. 1 The empty structure is ''disconnected'' and the definition of a tree is ''connected acyclic graph''. For example to get from the generating series G(t) of a connected species to the generating series of the set of its structures  G^(t)  the formula is$$ G^(t) = \exp(G^*(t)) = 1 + ... . This'$1$' at degree zero is the empty structure.