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A036295
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Numerator of Sum_{i=1..n} i/2^i.
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4
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0, 1, 1, 11, 13, 57, 15, 247, 251, 1013, 509, 4083, 4089, 16369, 2047, 65519, 65527, 262125, 131067, 1048555, 1048565, 4194281, 1048573, 16777191, 16777203, 67108837, 33554425, 268435427, 268435441, 1073741793, 67108863, 4294967263, 4294967279, 17179869149
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OFFSET
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0,4
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REFERENCES
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C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 95.
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LINKS
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FORMULA
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a(n) = numerator(2-(n+2)/2^n).
If n+2=2^k*m with m odd, then a(n) = 2^(n+1-k) - m.
Numerators of coefficients in expansion of 2*x / ((1 - x) * (2 - x)^2). - Ilya Gutkovskiy, Aug 04 2023
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MAPLE
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MATHEMATICA
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a[n_] := Module[{k, m}, For[k = 0; m = n + 2, EvenQ[m], k++, m/=2]; 2^(n + 1 - k) - m]
Table[Numerator[Sum[i/2^i, {i, n}]], {n, 40}] (* Alonso del Arte, Aug 12 2012 *)
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PROG
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(PARI) concat(0, vector(100, n, numerator(sum(i=1, n, i/2^i)))) \\ Colin Barker, Nov 09 2014
(PARI) a(n) = numerator(2-(n+2)/2^n); \\ Joerg Arndt, Jul 17 2023
(Magma) [0] cat [Numerator(&+[i/2^i: i in [1..n]]): n in [1..40]]; // Vincenzo Librandi, Nov 09 2014
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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