A282245 a(n) = 1/n times the number of n-colorings of the complete bipartite graph K_(n,n).

0, 1, 14, 453, 25444, 2214105, 276079026, 46716040525, 10304669487848, 2872910342870577, 987880924373494150, 410733590889633758901, 203120943850262404686732, 117838575503522957479230601, 79257755538247144929720855674, 61179085294923281767500772446045

Offset: 1

Author

Alois P. Heinz, Feb 09 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..228
• Eric Weisstein's World of Mathematics, Complete Bipartite Graph
• Wikipedia, Chromatic Polynomial

Crossrefs

Cf. A008277, A212085.

Programs

Maple

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

Formula

a(n) = 1/n * Sum_{j=1..n} (n-j)^n * Stirling2(n,j) * Product_{i=0..j-1} (n-i).

a(n) = 1/n * A212085(n,n).

a(n) ~ c * d^n * n^(2*n-1) / exp(2*n), where d = 3.42422933454838937778530870500341391459244769750638251404159... and c = 0.646741403357125093928623036806787050141001... . - Vaclav Kotesovec, Feb 18 2017