A cograph is a graph without induced $P\_4$ subgraphs. I am looking for a reference for a simple exponential bound on the number of distinct unlabeled cographs on $n$ vertices. By [the Mathworld article on cographs](http://mathworld.wolfram.com/Cograph.html) this is the same as the number of series-parallel networks with $n$ unlabeled edges. Judging from the first couple of terms in the list, the bound should be something like $3^n$. Any reference to a simple, exponential bound in closed-form would be much appreciated.



Bound on the number of unlabeled cographs on n vertices
Let your sequence be $a\_n$ for the number of series-parallel networks with $n$ unlabeled edges. The following identity of generating functions holds
$$1+\sum\_{k=1}^{\infty}a\_kx^k=\left[\frac{1}{(1-x)}\prod\_{k\geq 1}\frac{1}{(1-x^k)^{a\_k}}\right]^{1/2}$$ from which the asymptotics
$$a\_n\sim C d^n n^{-3/2}$$ follow, where $C=0.4126...$, $d=3.56083930953894...$


See also the article "Some enumerative results on series parallel networks" by J.W. Moon.


