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A132076
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a(1)=1, a(2)=2. a(n), for every positive integer n, is such that product{k=1 to n} (sum{j=1 to k} a(j)) = sum{k=1 to n} product{j=1 to k} a(j).
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0
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1, 2, -6, -12, -240, -65280, -4294901760, -18446744069414584320, -340282366920938463444927863358058659840, -115792089237316195423570985008687907852929702298719625575994209400481361428480
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| There are an infinite number of sequences {a(k)}, with different values for a(1) and a(2) (a(1) must be 0 or 1; a(2) can be anything), where product{k=1 to n} (sum{j=1 to k} a(j)) = sum{k=1 to n} product{j=1 to k} a(j), for all positive integers n. Setting a(1) to 1 and a(2) to 2 results in the sequence here.
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FORMULA
| For n >= 4, a(n) = -2^(2^(n-3)) * (2^(2^(n-3)) - 1).
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EXAMPLE
| For n = 4, we have a(1) * (a(1)+a(2)) * (a(1)+a(2)+a(3)) * (a(1)+a(2)+a(3)+a(4)) = a(1) + a(1)*a(2) + a(1)*a(2)*a(3) + a(1)*a(2)*a(3)*a(4) =
1 * (1+2) * (1+2-6) * (1+2-6-12) = 1 + 1*2 + 1*2*(-6) + 1*2*(-6)*(-12) = 135.
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CROSSREFS
| Sequence in context: A195338 A179201 A105122 * A058046 A192321 A074180
Adjacent sequences: A132073 A132074 A132075 * A132077 A132078 A132079
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KEYWORD
| easy,sign
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AUTHOR
| Leroy Quet Oct 30 2007
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Apr 29 2010
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