A152684 a(n) is the number of top-down sequences (F_1, F_2, ..., F_n) whereas each F_i is a labeled forest on n nodes, containing i directed rooted trees. F_(i+1) is proper subset of F_i.

1, 2, 18, 384, 15000, 933120, 84707280, 10569646080, 1735643790720, 362880000000000, 94121726392108800, 29658516531078758400, 11159820050604594969600, 4942478402320838374195200, 2544989406021562500000000000, 1507645899890367707813511168000

Offset: 1

Author

Fabian Nedic, Dec 10 2008

Keywords

• nonn

Examples

			a(1) = 1^(1-2)*(1!) = 1.
a(2) = 2^(2-2)*(2!) = 2.
a(3) = 3^(3-2)*(3!) = 18.
		

References

• Miklos Bona, Introduction to Enumerative Combinatorics, McGraw Hill 2007, Page 276.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A061711, A066319, A137268.

Programs

Magma

[Factorial(n-1)*n^(n-1): n in [1..20]]; // G. C. Greubel, Nov 28 2022

Maple

a:= proc(n) option remember; `if`(n=1, 1,
      a(n-1)*(n/(n-1))^(n-3)*n^2)
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, May 16 2013

Mathematica

Table[n^(n - 1) (n - 1)!, {n, 1, 16}]  (* Geoffrey Critzer, May 10 2013 *)

SageMath

[factorial(n-1)*n^(n-1) for n in range(1,21)] # G. C. Greubel, Nov 28 2022

Formula

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