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A348373 Decimal expansion of Sum_{k>=1} H(k)^2/2^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. 0
2, 1, 2, 5, 3, 8, 7, 0, 8, 0, 7, 6, 6, 4, 2, 7, 8, 6, 1, 1, 3, 9, 5, 1, 7, 6, 9, 2, 9, 7, 2, 6, 9, 0, 1, 6, 0, 9, 4, 9, 5, 0, 2, 8, 5, 2, 8, 0, 1, 3, 4, 4, 0, 2, 4, 6, 0, 2, 4, 2, 2, 3, 6, 2, 9, 9, 3, 6, 7, 2, 8, 5, 2, 6, 6, 3, 0, 3, 5, 3, 4, 6, 0, 3, 3, 5, 7, 7, 1, 6, 4, 0, 6, 3, 6, 8, 5, 6, 9, 6, 2, 3, 6, 7, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

István Mező, A q-Raabe formula and an integral of the fourth Jacobi theta function, Journal of Number Theory, Vol. 133, No. 2 (2013), pp. 692-704.

Seán Mark Stewart, Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers, Tatra Mountains Mathematical Publications, Vol. 77, No. 1 (2020), pp. 73-98.

FORMULA

Equals Pi^2/6 + log(2)^2 = A013661 + A253191.

EXAMPLE

2.12538708076642786113951769297269016094950285280134...

MATHEMATICA

RealDigits[Pi^2/6 + Log[2]^2, 10, 100][[1]]

CROSSREFS

Cf. A001008, A002805, A013661, A103930, A103931, A253191.

Similar constants: A016627, A076788.

Sequence in context: A212431 A346517 A318354 * A106480 A099602 A151703

Adjacent sequences:  A348370 A348371 A348372 * A348374 A348375 A348376

KEYWORD

nonn,cons,easy

AUTHOR

Amiram Eldar, Oct 15 2021

STATUS

approved

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)