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 A282247 a(n) = 1/(2*n) times the number of n-colorings of the complete tripartite graph K_(k,k,k). 2
 0, 0, 1, 66, 9546, 2995540, 1569542955, 1261871330286, 1497794187367828, 2511721997105517288, 5733323495739849790485, 17312353700125621441996450, 67543299290149425529497170526, 333695384900672678963632331684412, 2052058288990669598319358806485894719 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..174 Eric Weisstein's World of Mathematics, Complete Tripartite Graph Wikipedia, Chromatic Polynomial FORMULA a(n) = 1/(2*n) * Sum_{j,m=1..n} S2(n,j) * S2(n,m) * (n-j-m)^n * Product_{i=0..j+m-1} (n-i) with S2 = A008277. a(n) = A212221(n,n). a(n) ~ c * d^n * n!^3 / n^(5/2), where d = 2.1534859143209968... and c = 0.008659981748969... . - Vaclav Kotesovec, Feb 18 2017 MAPLE a:= n-> add(add(Stirling2(n, k)*Stirling2(n, m)*     mul(n-i, i=0..k+m-1)*(n-k-m)^n, m=1..n), k=1..n)/(2*n): seq(a(n), n=1..20); CROSSREFS Main diagonal of A212221. Cf. A008277. Sequence in context: A003555 A283222 A093266 * A197439 A127706 A167778 Adjacent sequences:  A282244 A282245 A282246 * A282248 A282249 A282250 KEYWORD nonn AUTHOR Alois P. Heinz, Feb 09 2017 STATUS approved

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Last modified January 25 09:50 EST 2022. Contains 350565 sequences. (Running on oeis4.)