We call progressive paths and rushed paths two families of Dyck paths studied by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry A287709). We present a bijection proving this fact. Rushed paths turn out to be in bijection with one-sided trees, introduced by Durhuus and Unel, which have an asymptotic enumeration involving a stretched exponential. We conclude by presenting several other classes of related lattice paths and directed animals that may have similar asymptotic properties.

翻译：我们称由Asinowski和Jelinek研究的两类Dyck路径为渐进路径和急促路径，这两类路径具有相同的计数序列（OEIS条目A287709）。我们给出一个双射来证明这一事实。最终证明，急促路径与由Durhuus和Unel引入的单侧树之间存在双射关系，后者的渐近计数涉及一种拉伸指数。最后，我们介绍了其他几类可能具有类似渐近性质的格点路径和有向动物。