A322754 Number of unlabeled 7-trees on n nodes.

0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 5, 15, 64, 342, 2344, 19137, 181098, 1922215, 22472875, 284556458, 3849828695, 54974808527, 819865209740, 12655913153775, 200748351368185, 3253193955012557, 53619437319817482, 895778170144927928, 15129118461773051724

Offset: 1

Author

N. J. A. Sloane, Dec 26 2018

Keywords

• nonn

Comments

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.

References

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

Links

• Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
• Andrew Gainer-Dewar, Gamma-Species and the Enumeration of k-Trees, Electronic Journal of Combinatorics, Volume 19 (2012), #P45.

Crossrefs

Column k=7 of A370770.

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