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A274031 Decimal expansion of a doubly infinite sum involving harmonic numbers. Curiously, this sum is very close to 1. 0
9, 9, 9, 2, 2, 2, 8, 3, 7, 7, 6, 3, 8, 3, 0, 0, 0, 8, 7, 6, 1, 9, 3, 5, 7, 4, 9, 2, 4, 7, 5, 6, 9, 8, 8, 6, 0, 3, 6, 9, 9, 5, 5, 1, 6, 1, 3, 6, 1, 7, 0, 9, 4, 4, 2, 0, 4, 8, 9, 8, 4, 3, 5, 8, 6, 2, 7, 6, 1, 0, 2, 2, 9, 7, 3, 5, 5, 0, 1, 2, 4, 2, 2, 2, 1, 9, 6, 3, 5, 3, 5, 0, 3, 5, 5, 9, 7, 6, 4, 7, 3, 9, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..102.

R. Pemantle, C. Schneider, When is 0.999... equal to 1?,  arXiv:math/0511574 [math.CO], 2005.

FORMULA

Sum_{j >= 1, k >= 1} H(j) (H(k+1)-1)/(j k (k+1) (j+k)), where H(j) is the j-th harmonic number.

Equals -4 zeta(2) - 2 zeta(3) + 4 zeta(2) zeta(3) + 2 zeta(5).

EXAMPLE

0.99922283776383000876193574924756988603699551613617094420489843586276...

MATHEMATICA

RealDigits[-4 Zeta[2] - 2 Zeta[3] + 4 Zeta[2] Zeta[3] + 2 Zeta[5], 10,

   103][[1]]

CROSSREFS

Sequence in context: A109942 A339745 A197149 * A111623 A229985 A019897

Adjacent sequences:  A274028 A274029 A274030 * A274032 A274033 A274034

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jun 07 2016

STATUS

approved

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Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)