login
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
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Complete Bipartite Graph
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
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
Sequence in context: A103916 A201546 A305115 * A319096 A297548 A215787
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 09 2017
STATUS
approved