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A282245
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a(n) = 1/n times the number of n-colorings of the complete bipartite graph K_(n,n).
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2
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0, 1, 14, 453, 25444, 2214105, 276079026, 46716040525, 10304669487848, 2872910342870577, 987880924373494150, 410733590889633758901, 203120943850262404686732, 117838575503522957479230601, 79257755538247144929720855674, 61179085294923281767500772446045
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = 1/n * Sum_{j=1..n} (n-j)^n * Stirling2(n,j) * Product_{i=0..j-1} (n-i).
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
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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