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A348563 Decimal expansion of Sum_{k>=1} H(k) * binomial(2*k,k)/((2*k+1)*4^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. 0
1, 4, 8, 6, 2, 7, 6, 2, 8, 6, 4, 0, 5, 2, 7, 3, 9, 2, 9, 7, 1, 7, 7, 2, 5, 1, 6, 1, 4, 9, 1, 9, 2, 2, 4, 9, 5, 7, 5, 8, 0, 1, 3, 7, 9, 6, 7, 5, 7, 4, 0, 2, 2, 4, 2, 7, 4, 0, 1, 9, 7, 2, 2, 5, 2, 9, 2, 7, 4, 3, 5, 2, 9, 9, 2, 8, 2, 7, 7, 0, 9, 1, 4, 8, 7, 0, 9, 7, 0, 9, 0, 0, 9, 3, 7, 9, 7, 3, 9, 9, 9, 3, 6, 6, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Amrik Singh Nimbran, Sums of series involving central binomial coefficients and harmonic numbers, The Mathematics Student, Vol. 88, No. 1-2 (2019), pp. 125-135; arXiv preprint, arXiv:1806.03998 [math.NT], 2018-2019.
FORMULA
Equals 4*G - Pi*log(2), where G is Catalan's constant (A006752).
Equals Integral_{-Pi/2 .. Pi/2} log(1+cos(x)) dx. - Philippe Deléham , Jan 12 2024
EXAMPLE
1.48627628640527392971772516149192249575801379675740...
MATHEMATICA
RealDigits[4*Catalan - Pi*Log[2], 10, 100][[1]]
CROSSREFS
Sequence in context: A198241 A175475 A193082 * A201335 A338942 A219246
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Oct 22 2021
STATUS
approved

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Last modified May 22 09:57 EDT 2024. Contains 372745 sequences. (Running on oeis4.)