  We study the class of graphs known as k-trees through the lens of Joyal's
theory of combinatorial species (and an equivariant extension known as
'$\Gamma$-species' which incorporates data about 'structural' group actions).
This culminates in a system of recursive functional equations giving the
generating function for unlabeled k-trees which allows for fast, efficient
computation of their numbers. Enumerations up to k = 10 and n = 30 (for a
k-tree with (n+k-1) vertices) are included in tables, and Sage code for the
general computation is included in an appendix.
