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A182553
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Chromatic invariant of the complete tripartite graph K_(n,n,n).
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2
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1, 11, 1243, 490043, 463370491, 860454250571, 2769263554592683, 14178247400433059003, 108483732651999512059291, 1182804548772797481324575531, 17700419121823142496192223238923, 352709466470858225716888461028622363, 9127611521817307582541815420363992765691
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OFFSET
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1,2
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COMMENTS
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The chromatic invariant equals the absolute value of the first derivative of the chromatic polynomial evaluated at 1.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..60
Eric Weisstein's World of Mathematics, Chromatic Invariant
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Wikipedia, Chromatic Polynomial
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FORMULA
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a(n) = |(d/dq P(n,q))_{q=1}| with P(n,q) = Sum_{k,m=1..n} S2(n,k) * S2(n,m) * (q-k-m)^n * Product_{i=0..k+m-1} (q-i) and S2 = A008277.
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MAPLE
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with (combinat):
P:= n-> expand (add (add (stirling2(n, k) *stirling2(n, m)
*mul(q-i, i=0..k+m-1) *(q-k-m)^n, m=1..n), k=1..n)):
a:= n-> abs (subs (q=1, diff (P(n), q))):
seq (a(n), n=1..15);
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CROSSREFS
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Cf. A008277, A048144.
Sequence in context: A015009 A068326 A001323 * A223039 A209093 A078274
Adjacent sequences: A182550 A182551 A182552 * A182554 A182555 A182556
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, May 04 2012
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STATUS
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approved
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