A066319 A labeled structure simultaneously a tree and a cycle.

1, 1, 6, 96, 3000, 155520, 12101040, 1321205760, 192849310080, 36288000000000, 8556520581100800, 2471543044256563200, 858447696200353459200, 353034171594345598156800, 169665960401437500000000000

Offset: 1

Author

Christian G. Bower, Dec 13 2001

Keywords

• nonn

References

• F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 68 (2.1.37).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..230
• D. E. Knuth, A recurrence related to trees, Proc. Amer. Math. Soc. 105 (1989), 335-349. Reprinted as Chapter 39 of Selected Papers on Discrete Mathematics by D. E. Knuth.
• Thorsten Weist, On the Euler characteristic of Kronecker moduli spaces, arXiv preprint arXiv:1203.2740 [math.RT], 2012. Cor. 5.3, k=1. But offset 0.
• Index entries for sequences related to trees

Programs

Magma

[n^(n-3)*Factorial(n): n in [1..20]]; // G. C. Greubel, May 29 2019

Mathematica

Table[n!*n^(n-3), {n,1,20}] (* G. C. Greubel, May 29 2019 *)

PARI

a(n) = n^(n-2)*(n-1)!; \\ Michel Marcus, May 29 2019

Sage

[n^(n-3)*factorial(n) for n in (1..20)] # G. C. Greubel, May 29 2019

Formula

a(n) = n^(n-2)*(n-1)!.

Extensions

Knuth reference from David Callan, Feb 07 2004