login
Number of assembly trees for the complete tripartite graph K_{n,n,n}.
2

%I #12 Jan 03 2025 03:43:53

%S 3,672,1065960,5384957760,62421991632000,1384386516152640000,

%T 52302971661503603040000,3105288818333100374976000000,

%U 273018704366102767367501606400000,33963457896477610629976094607360000000

%N Number of assembly trees for the complete tripartite graph K_{n,n,n}.

%H Andrew Vince and Miklos Bona, <a href="https://arxiv.org/abs/1204.3842">The Number of Ways to Assemble a Graph</a>, arXiv preprint, arXiv:1204.3842 [math.CO], 2012. See Theorem 23.

%H Andrew Vince and Miklos Bona, <a href="https://doi.org/10.37236/2644">The Number of Ways to Assemble a Graph</a>, The Electronic Journal of Combinatorics, Volume 19, Issue 4 (2012), Article P54.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AssemblyNumber.html">Assembly Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>

%t Table[n!^3 SeriesCoefficient[1 - Sqrt[(1 - x)^2 + (1 - y)^2 + (1 - z)^2 - 2], {x, 0, n}, {y, 0, n}, {z, 0, n}], {n, 10}]

%Y Cf. A217523 (number of assembly trees for K_{n,n})

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Mar 01 2023