Conjecture on polynomial-time enumeration of regular graphs

Fix $k greater than or equal to 1$ and let $a_n$ be the number of unlabeled $k$-regular graphs with $n$ vertices.

Regular-graph enumeration conjecture. The sequence $a_n$ can be computed in polynomial time in $n$.

The source notes polynomial recurrences for labeled $k$-regular graphs for each fixed $k$, but does not establish the corresponding claim for unlabeled graphs. No resolution is supplied.