  Partially ordered sets have received much attention in recent years, not just
due to their usefulness in combinatorics and abstract algebra, but also due to
their practical applications in fields ranging from chemistry to
macroeconomics. The garland or double fence $G_N$ is a partially ordered set
with $2N$ elements which generalizes the well-known fence or zigzag poset. The
main result of this paper is recurrence relations for enumerating the linear
extensions of $G_N$. These recurrences were then applied to prove divergence of
the standard type $G_N$-generating series. When coded in Python, it provides a
fast method for computing $e(G_n)$ for arbitrary $n$. The first 200 terms of
this sequence are published online under OEIS A227656.
