A082787 a(n) = (2/3)*(2*n-1)!*binomial(3*n,2*n).

2, 60, 6720, 1663200, 726485760, 494010316800, 482718652416000, 641171050071552000, 1111363153457356800000, 2436552577639909048320000, 6591982246414881207091200000, 21572261901392698750205952000000, 83992431415453295380032651264000000, 383725422380885198036206312488960000000

Offset: 1

Author

N. J. A. Sloane, May 22 2003

Keywords

• nonn

Comments

A solid 2-tree is a 2-tree embedded in three-dimensional space. That is, the faces of the triangles cannot interpenetrate themselves, so that there is a cyclic configuration of triangles around every edge. Bousquet and Lamathe showed the number of well-oriented edge-labeled solid 2-trees with 2n+1 edges is a(n). - Allan Bickle, Feb 19 2024

Links

• Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.
• M. Bousquet and C. Lamathe, Enumeration of solid trees according to edge number and edge degree distribution, Discr. Math., 298 (2005), 115-141.

Programs

Mathematica

Table[(2(2n-1)!Binomial[3n,2n])/3,{n,20}] (* Harvey P. Dale, May 28 2014 *)