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A282245 a(n) = 1/n times the number of n-colorings of the complete bipartite graph K_(n,n). 2
0, 1, 14, 453, 25444, 2214105, 276079026, 46716040525, 10304669487848, 2872910342870577, 987880924373494150, 410733590889633758901, 203120943850262404686732, 117838575503522957479230601, 79257755538247144929720855674, 61179085294923281767500772446045 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

FORMULA

a(n) = 1/n * Sum_{j=1..n} (n-j)^n * S2(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

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);

CROSSREFS

Cf. A008277, A212085.

Sequence in context: A103916 A201546 A305115 * A319096 A297548 A215787

Adjacent sequences:  A282242 A282243 A282244 * A282246 A282247 A282248

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 09 2017

STATUS

approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)