A283261 Product of the different products of subsets of the set of numbers from 1 to n.

1, 1, 2, 36, 331776, 42998169600000000, 13974055172471046820331520000000000000, 1833132881579690383668380351534446872452674453158326975200092938148249600000000000000000000000000

Offset: 0

Author

Jaroslav Krizek, Mar 04 2017

Keywords

• nonn

Comments

Product of numbers in n-th row of A070861.

Examples

			Rows with subsets of the sets of numbers from 1 to n:
  {},
  {}, {1};
  {}, {1}, {2}, {1, 2};
  {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3};
  ...
Rows with the products of elements of these subsets:
  1;
  1, 1;
  1, 1, 2, 2;
  1, 1, 2, 3, 2, 3, 6, 6;
  ...
Rows with the different products of elements of these subsets:
  1;
  1;
  1, 2;
  1, 2, 3, 6;
  ...
a(0) = 1, a(1) = (1), a(2) = (1*2) = 2, a(3) = (1*2*3*6) = 36, ... .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10

Crossrefs

Cf. A000005, A000142, A027423, A060957, A070863, A052295, A263292.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, {1},
      map(x-> [x, x*n][], b(n-1)))
    end:
a:= n-> mul(i, i=b(n)):
seq(a(n), n=0..7);  # Alois P. Heinz, Aug 01 2022

Mathematica

Table[Times @@ Union@ Map[Times @@ # &, Subsets@ Range@ n], {n, 7}] (* Michael De Vlieger, Mar 05 2017 *)

PARI

a(n)=my(v=[2..n]); factorback(Set(vector(2^(n-1),i, factorback(vecextract(v,i-1))))) \\ Charles R Greathouse IV, Mar 06 2017

Formula

a(n) <= n!^((A000005(n!))/2) = n!^(A027423(n)/2). - David A. Corneth, Mar 05 2017

a(n) = n!^(A263292(n)). - David A. Corneth, Mar 06 2017

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 01 2022