A282247 a(n) = 1/(2*n) times the number of n-colorings of the complete tripartite graph K_(k,k,k).

0, 0, 1, 66, 9546, 2995540, 1569542955, 1261871330286, 1497794187367828, 2511721997105517288, 5733323495739849790485, 17312353700125621441996450, 67543299290149425529497170526, 333695384900672678963632331684412, 2052058288990669598319358806485894719

Offset: 1

Author

Alois P. Heinz, Feb 09 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..174
• Eric Weisstein's World of Mathematics, Complete Tripartite Graph
• Wikipedia, Chromatic Polynomial

Crossrefs

Main diagonal of A212221.

Cf. A008277.

Programs

Maple

a:= n-> add(add(Stirling2(n, k)*Stirling2(n, m)*
    mul(n-i, i=0..k+m-1)*(n-k-m)^n, m=1..n), k=1..n)/(2*n):
seq(a(n), n=1..20);

Formula

a(n) = 1/(2*n) * Sum_{j,m=1..n} S2(n,j) * S2(n,m) * (n-j-m)^n * Product_{i=0..j+m-1} (n-i) with S2 = A008277.

a(n) = A212221(n,n).

a(n) ~ c * d^n * n!^3 / n^(5/2), where d = 2.1534859143209968... and c = 0.008659981748969... . - Vaclav Kotesovec, Feb 18 2017