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A110625
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Numerator of b(n) = -Sum(k=1 to n, A037861(k)/((2k)(2k+1))), where A037861(k) = (number of 0's) - (number of 1's) in binary representation of k.
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5
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1, 1, 3, 101, 5807, 77801, 82949, 170636, 170636, 170636, 363113, 363113, 84848, 710567, 22435781, 3901243741, 27210449083, 1003538672911, 248595095590537, 10165684261926701, 438167567023512863, 439119040574907047
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Numerators of partial sums of a series for the "alternating Euler constant" log(4/Pi) (see A094640 and Sondow 2005, 2010). Denominators are A110626.
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LINKS
| J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005) 61-65.
J. Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi), Additive Number Theory, Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson (D. Chudnovsky and G. Chudnovsky, eds.), Springer, 2010, pp. 331-340.
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FORMULA
| lim(n -> infinity, b(n)) = log 4/Pi = 0.24156...
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EXAMPLE
| a(3) = 3 because b(3) = 1/6 + 0 + 1/21 = 3/14.
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CROSSREFS
| Cf. A037861, A073099, A094640, A110626.
Sequence in context: A037114 A069457 A142416 * A108220 A130733 A037062
Adjacent sequences: A110622 A110623 A110624 * A110626 A110627 A110628
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KEYWORD
| easy,frac,nonn
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AUTHOR
| Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 01 2005
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