login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A283261 Product of the different products of subsets of the set of numbers from 1 to n. 3
1, 1, 2, 36, 331776, 42998169600000000, 13974055172471046820331520000000000000, 1833132881579690383668380351534446872452674453158326975200092938148249600000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Product of numbers in n-th row of A070861.
LINKS
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
EXAMPLE
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, ... .
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 *)
PROG
(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
CROSSREFS
Sequence in context: A326961 A181555 A306644 * A280420 A051459 A358972
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 04 2017
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Aug 01 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 14 16:00 EDT 2024. Contains 371665 sequences. (Running on oeis4.)