A208661 Number of paths through the subset array of {1,2,...,n} that have range a subset of {1,2}; see Comments at A208650.

1, 4, 16, 144, 3072, 160000, 20736000, 6776582400, 5639493386240, 12041750911647744, 66367674777600000000, 948747002032456704000000, 35319813420678024297185280000, 3435829941215659552226769213849600

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Example

For n=4, write
row 1:  1; 2; 3; 4
row 2:  1,2; 1,3; 1,4; 2,3; 2,4; 3,4
row 3:  1,2,3; 1,2,4; 1,3,4; 2,3,4
row 4:  1,2,3,4
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.

Mathematica

a[1] = 1; z = 15;
a[n_] := (2^n)*Product[Binomial[n - 1, i], {i, 1, n - 1}]
Table[a[n], {n, 1, z}]  (* A208661 *)

Crossrefs

Cf. A208650.

Sequence in context: A319166 A335400 A304193 * A334746 A262123 A005749

Adjacent sequences: A208658 A208659 A208660 * A208662 A208663 A208664

Keyword

nonn

Author

Clark Kimberling, Mar 02 2012

Status

approved