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

1,1

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

Table of n, a(n) for n=1..14.

Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs, Vol. 0, Iss. 1 (2024), Article 5.

Michel Bousquet and Cédric Lamathe, Enumeration of solid trees according to edge number and edge degree distribution, Discr. Math., 298 (2005), 115-141.

Formula

a(n) ~ 3^(3*n-1/2) * n^(2*n-1) / exp(2*n). - Amiram Eldar, Sep 19 2025

Mathematica

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

Crossrefs

Cf. A005809.

Sequence in context: A056923 A173221 A375840 * A078423 A231024 A356584

Adjacent sequences: A082784 A082785 A082786 * A082788 A082789 A082790

Keyword

nonn,easy

Author

N. J. A. Sloane, May 22 2003

Status

approved