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

 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 Alois P. Heinz, Table of n, a(n) for n = 0..10 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 Cf. A000005, A000142, A027423, A060957, A070863, A052295, A263292. Sequence in context: A326961 A181555 A306644 * A280420 A051459 A358972 Adjacent sequences: A283258 A283259 A283260 * A283262 A283263 A283264 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.

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