Is there a formula for finding the number of nonisomorphic simple graphs that have n nodes?
Solution 1:
This is OEIS A000088. Two asymptotic formulas are given, the first of which is
$$a(n)=\frac{2^{\binom{n}2}}{n!}\left(1+\frac{n^2-n}{2^{n-1}}+\frac{8n!(3n-7)(3n-9)}{2^{2n}(n-4)!}\right)+O\left(\frac{n^5}{2^{5n/2}}\right)\;,$$
but there does not appear to be a nice closed form.