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Number of unlabeled 7-trees on n nodes.
1

%I #18 Mar 02 2024 12:01:12

%S 0,0,0,0,0,0,1,1,1,2,5,15,64,342,2344,19137,181098,1922215,22472875,

%T 284556458,3849828695,54974808527,819865209740,12655913153775,

%U 200748351368185,3253193955012557,53619437319817482,895778170144927928,15129118461773051724

%N Number of unlabeled 7-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.

%Y Column k=7 of A370770.

%Y Cf. A054581 (unlabeled 2-trees), A078792 (unlabeled 3-trees), A078793 (unlabeled 4-trees), A201702 (unlabeled 5-trees), A202037 (unlabeled 6-trees).

%K nonn

%O 1,10

%A _N. J. A. Sloane_, Dec 26 2018