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Number of unlabeled 6-trees on n nodes.
3

%I #28 Mar 02 2024 12:01:28

%S 0,0,0,0,0,1,1,1,2,5,15,64,342,2344,19090,179562,1878277,21365403,

%T 258965451,3294561195,43472906719,589744428065,8171396893523,

%U 115094557122380,1642269376265063,23679803216530017,344396036645439675,5045351124912000756

%N Number of unlabeled 6-trees on n nodes.

%C A k-tree is recursively defined as follows: K_k is a k-tree and any k-tree on n+1 vertices is obtained by joining a vertex to a k-clique in a k-tree on n vertices.

%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 328.

%H Allan Bickle, <a href="https://doi.org/10.20429/tag.2024.000105">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.

%H Andrew Gainer-Dewar, <a href="https://doi.org/10.37236/2615">Gamma-Species and the Enumeration of k-Trees</a>, Electronic Journal of Combinatorics, Volume 19 (2012), #P45. - From _N. J. A. Sloane_, Dec 15 2012

%Y Column k=6 of A370770.

%Y Cf. A054581 (unlabeled 2-trees), A078792 (unlabeled 3-trees), A078793 (unlabeled 4-trees), A201702 (unlabeled 5-trees)

%K nonn

%O 1,9

%A _Andrew R. Gainer_, Dec 09 2011