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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

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

Cf. A000984, A001008, A002805, A006752, A086054.

Sequence in context: A198241 A175475 A193082 * A201335 A338942 A219246

Adjacent sequences: A348560 A348561 A348562 * A348564 A348565 A348566

Keyword

nonn,cons

Author

Amiram Eldar, Oct 22 2021

Status

approved