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A110626
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Denominator 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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4
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6, 6, 14, 504, 27720, 360360, 360360, 765765, 765765, 765765, 1601145, 1601145, 369495, 3061530, 94907430, 16703707680, 116925953760, 4326260289120, 1068586291412640, 43812037947918240, 1883917631760484320
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Denominators of partial sums of a series for the "alternating Euler constant" log(4/Pi) (see A094640 and Sondow 2005, 2010). Numerators are A110625.
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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) = 14 because b(3) = 1/6 + 0 + 1/21 = 3/14.
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CROSSREFS
| Cf. A037861, A073099, A094640, A110625.
Sequence in context: A141378 A003871 A168384 * A072695 A085596 A107620
Adjacent sequences: A110623 A110624 A110625 * A110627 A110628 A110629
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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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