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A174881
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Number of admissible graphs of order n.
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2
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2, 36, 1728, 160000, 24300000, 5489031744, 1727094849536, 722204136308736, 387420489000000000, 259374246010000000000, 211988959518950443450368, 207728067204059288762843136, 240396446553194784543350546432
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OFFSET
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1,1
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COMMENTS
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In Kontsevich, by definition, an admissible graph of order n is an ordered pair of maps i; j : {1, 2, 3, ..., n} --> {1, 2, 3, ..., n, L, R} where neither map has fixed points and both maps are distinct at every point. See p.18 of Dimofte.
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REFERENCES
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M. Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003), no. 3 157{216, [q-alg/9709040v1].
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LINKS
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Table of n, a(n) for n=1..13.
Tudor Dimofte, Sergei Gukov, Quantum Field Theory and the Volume Conjecture , March 26, 2010.
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FORMULA
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a(n) = (n^n)*((n+1)^n) = (n*(n+1))^n. = A000312(n)*A000169(n+1).
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EXAMPLE
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a(1) = (1^1)*((1+1)^1) = 2.
a(2) = (2^2)*((2+1)^2) = 36.
a(3) = (3^3)*((3+1)^3) = 1728.
a(4) = (4^4)*((4+1)^4) = 160000.
a(5) = (5^5)*((5+1)^5) = 24300000.
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CROSSREFS
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Cf. A000169, A000312.
Sequence in context: A174580 A209803 A088026 * A126934 A303503 A178949
Adjacent sequences: A174878 A174879 A174880 * A174882 A174883 A174884
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Mar 31 2010
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STATUS
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approved
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