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A283261
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Product of the different products of subsets of the set of numbers from 1 to n.
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3
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1, 1, 2, 36, 331776, 42998169600000000, 13974055172471046820331520000000000000, 1833132881579690383668380351534446872452674453158326975200092938148249600000000000000000000000000
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OFFSET
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0,3
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COMMENTS
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Product of numbers in n-th row of A070861.
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LINKS
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FORMULA
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EXAMPLE
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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, ... .
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MAPLE
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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)):
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MATHEMATICA
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Table[Times @@ Union@ Map[Times @@ # &, Subsets@ Range@ n], {n, 7}] (* Michael De Vlieger, Mar 05 2017 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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