cp's OEIS Frontend

A208651 Number of paths through the subset array whose trace is a permutation of (1,2,...,n); see Comments.

%I A208651 #8 Feb 25 2018 22:52:46
%S A208651 1,2,12,216,11520,1800000,816480000,1067311728000,3996990937497600,
%T A208651 42672954793151692800,1293547461212160000000000,
%U A208651 110950032218933108678400000000,26847804299643702075375747072000000
%N A208651 Number of paths through the subset array whose trace is a permutation of (1,2,...,n); see Comments.
%C A208651 See A208650.  The trace of a path is a permutation of (1,2,...,n) if and only if the range of the path is {1,2,...,n}.
%H A208651 Nick Early, <a href="https://arxiv.org/abs/1709.03686">Generalized Permutohedra, Scattering Amplitudes, and a Cubic Three-Fold</a>, arXiv:1709.03686 [math.CO], 2017.
%e A208651 Taking n=3:
%e A208651 row 1:  {1},{2},{3} ---------> 1,2,3
%e A208651 row 2:  {1,2},{1,3},{2,3} ---> 1,1,2,2,3,3
%e A208651 row 3:  {1,2,3} -------------> 1,2,3
%e A208651 3 ways to choose a number from row 1,
%e A208651 4 ways to choose a different number from row 2,
%e A208651 1 way to choose remaining number from row 3.
%e A208651 Total:  a(3) = 1*4*3 = 12 paths.
%t A208651 p[n_]:=Product[Binomial[n-1,k],{k,1,n-1}]
%t A208651 Table[p[n],{n,1,20}]    (* A001142(n-1) *)
%t A208651 Table[p[n]*n,{n,1,20}]  (* A208650 *)
%t A208651 Table[p[n]*n!,{n,1,20}] (* A208651 *)
%Y A208651 Cf. A208650.
%K A208651 nonn
%O A208651 1,2
%A A208651 _Clark Kimberling_, Mar 01 2012