login
A174881
a(n) = n^n * (n+1)^n.
3
2, 36, 1728, 160000, 24300000, 5489031744, 1727094849536, 722204136308736, 387420489000000000, 259374246010000000000, 211988959518950443450368, 207728067204059288762843136, 240396446553194784543350546432, 324391993252150868100000000000000
OFFSET
1,1
COMMENTS
a(n) is the number of ordered pairs 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. In Kontsevich, these are called admissible graphs.
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, arXiv:1003.4808 [math.GT], 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.
MATHEMATICA
Table[(n*(n + 1))^n, {n, 15}] (* Paolo Xausa, Oct 13 2024 *)
CROSSREFS
Sequence in context: A174580 A209803 A088026 * A126934 A303503 A178949
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 31 2010
STATUS
approved