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A174881 Number of admissible graphs of order n. 2
2, 36, 1728, 160000, 24300000, 5489031744, 1727094849536, 722204136308736, 387420489000000000, 259374246010000000000, 211988959518950443450368, 207728067204059288762843136, 240396446553194784543350546432 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
REFERENCES
M. Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003), no. 3 157{216, [q-alg/9709040v1].
LINKS
Tudor Dimofte, Sergei Gukov, Quantum Field Theory and the Volume Conjecture , March 26, 2010.
FORMULA
a(n) = (n^n)*((n+1)^n) = (n*(n+1))^n. = A000312(n)*A000169(n+1).
EXAMPLE
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.
CROSSREFS
Sequence in context: A174580 A209803 A088026 * A126934 A303503 A178949
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 31 2010
STATUS
approved

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Last modified May 26 01:22 EDT 2024. Contains 372807 sequences. (Running on oeis4.)