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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.
1
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
OFFSET
1,1
LINKS
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
Similar constants: A016627, A076788.
Sequence in context: A212431 A346517 A318354 * A106480 A099602 A151703
KEYWORD
nonn,cons,easy
AUTHOR
Amiram Eldar, Oct 15 2021
STATUS
approved