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A110626 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. 4
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; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..21.

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.

FORMULA

lim(n -> infinity, b(n)) = log 4/Pi = 0.24156...

EXAMPLE

a(3) = 14 because b(3) = 1/6 + 0 + 1/21 = 3/14.

CROSSREFS

Cf. A037861, A073099, A094640, A110625.

Sequence in context: A315806 A315807 A315808 * A072695 A085596 A107620

Adjacent sequences:  A110623 A110624 A110625 * A110627 A110628 A110629

KEYWORD

easy,frac,nonn

AUTHOR

Jonathan Sondow, Aug 01 2005

STATUS

approved

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Last modified November 21 16:04 EST 2019. Contains 329371 sequences. (Running on oeis4.)