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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

Table of n, a(n) for n=1..13.

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

Cf. A000169, A000312.

Sequence in context: A174580 A209803 A088026 * A126934 A178949 A200571

Adjacent sequences:  A174878 A174879 A174880 * A174882 A174883 A174884

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Mar 31 2010

STATUS

approved

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Last modified November 19 16:10 EST 2017. Contains 294936 sequences.