A152684 - OEIS

%I #23 Dec 01 2022 15:30:01

%S 1,2,18,384,15000,933120,84707280,10569646080,1735643790720,

%T 362880000000000,94121726392108800,29658516531078758400,

%U 11159820050604594969600,4942478402320838374195200,2544989406021562500000000000,1507645899890367707813511168000

%N 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.

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

%H Alois P. Heinz, <a href="/A152684/b152684.txt">Table of n, a(n) for n = 1..100</a>

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

%e a(1) = 1^(1-2)*(1!) = 1.

%e a(2) = 2^(2-2)*(2!) = 2.

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

%p a:= proc(n) option remember; `if`(n=1, 1,

%p       a(n-1)*(n/(n-1))^(n-3)*n^2)

%p     end:

%p seq(a(n), n=1..20);  # _Alois P. Heinz_, May 16 2013

%t Table[n^(n - 1) (n - 1)!, {n, 1, 16}]  (* _Geoffrey Critzer_, May 10 2013 *)

%o (Magma) [Factorial(n-1)*n^(n-1): n in [1..20]]; // _G. C. Greubel_, Nov 28 2022

%o (SageMath) [factorial(n-1)*n^(n-1) for n in range(1,21)] # _G. C. Greubel_, Nov 28 2022

%Y Cf. A061711, A066319, A137268.

%K nonn

%O 1,2

%A _Fabian Nedic_, Dec 10 2008