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%I #9 Aug 20 2022 19:53:30
%S 0,1,14,453,25444,2214105,276079026,46716040525,10304669487848,
%T 2872910342870577,987880924373494150,410733590889633758901,
%U 203120943850262404686732,117838575503522957479230601,79257755538247144929720855674,61179085294923281767500772446045
%N a(n) = 1/n times the number of n-colorings of the complete bipartite graph K_(n,n).
%H Alois P. Heinz, <a href="/A282245/b282245.txt">Table of n, a(n) for n = 1..228</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteBipartiteGraph.html">Complete Bipartite Graph</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic Polynomial</a>
%F a(n) = 1/n * Sum_{j=1..n} (n-j)^n * Stirling2(n,j) * Product_{i=0..j-1} (n-i).
%F a(n) = 1/n * A212085(n,n).
%F 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
%p a:= n-> add(Stirling2(n, j)*mul(n-i, i=0..j-1)*(n-j)^n, j=1..n)/n:
%p seq(a(n), n=1..20);
%Y Cf. A008277, A212085.
%K nonn
%O 1,3
%A _Alois P. Heinz_, Feb 09 2017
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