A208661 - OEIS

%I #9 Mar 30 2012 18:58:14

%S 1,4,16,144,3072,160000,20736000,6776582400,5639493386240,

%T 12041750911647744,66367674777600000000,948747002032456704000000,

%U 35319813420678024297185280000,3435829941215659552226769213849600

%N Number of paths through the subset array of {1,2,...,n} that have range a subset of {1,2}; see Comments at A208650.

%e For n=4, write

%e row 1:  1; 2; 3; 4

%e row 2:  1,2; 1,3; 1,4; 2,3; 2,4; 3,4

%e row 3:  1,2,3; 1,2,4; 1,3,4; 2,3,4

%e row 4:  1,2,3,4

%e There are 2 ways to choose 1 or 2 from row 1, then 6 ways to choose 1 or 2 from row 2, then 6 ways to choose 1 or 2 from row 3, then 2 ways to choose 1 or 2 from row 4, so that a(4)=2*6*6*2=144.

%t a[1] = 1; z = 15;

%t a[n_] := (2^n)*Product[Binomial[n - 1, i], {i, 1, n - 1}]

%t Table[a[n], {n, 1, z}]  (* A208661 *)

%Y Cf. A208650.

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 02 2012