A174881 a(n) = n^n * (n+1)^n.

2, 36, 1728, 160000, 24300000, 5489031744, 1727094849536, 722204136308736, 387420489000000000, 259374246010000000000, 211988959518950443450368, 207728067204059288762843136, 240396446553194784543350546432, 324391993252150868100000000000000

Offset: 1

Author

Jonathan Vos Post, Mar 31 2010

Keywords

• easy
• nonn

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.

Examples

			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.
		

References

• M. Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003), no. 3 157-216, [q-alg/9709040v1].

Links

• Paolo Xausa, Table of n, a(n) for n = 1..200
• Tudor Dimofte, Sergei Gukov, Quantum Field Theory and the Volume Conjecture, arXiv:1003.4808 [math.GT], 2010.

Crossrefs

Cf. A000169, A000312.

Programs

Mathematica

Table[(n*(n + 1))^n, {n, 15}] (* Paolo Xausa, Oct 13 2024 *)

Formula

a(n) = (n^n)*((n+1)^n) = (n*(n+1))^n = A000312(n)*A000169(n+1).