A348372 Decimal expansion of Sum_{k>=2} H(k)*H(k+1)/(k^3-k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

8, 8, 6, 7, 0, 9, 5, 8, 0, 1, 2, 8, 3, 4, 9, 1, 0, 5, 4, 8, 2, 1, 5, 8, 0, 4, 6, 8, 2, 7, 0, 4, 3, 7, 1, 1, 9, 3, 0, 2, 7, 6, 2, 3, 2, 3, 5, 7, 8, 0, 1, 5, 0, 8, 7, 7, 3, 8, 3, 8, 8, 8, 7, 3, 1, 5, 6, 5, 9, 9, 2, 6, 6, 1, 2, 8, 8, 6, 6, 9, 1, 3, 5, 5, 1, 3, 6, 9, 0, 1, 2, 3, 5, 7, 2, 5, 0, 6, 5, 5, 2, 7, 7, 9, 9

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Ovidiu Furdui and Alina Sȋntămărian, Problem 12060, The American Mathematical Monthly, Vol. 125, No. 7 (2018), p. 661; Summation by Parts and an Euler Sum, Solution to Problem 12060 by Omran Kouba, ibid., Vol. 127, No. 3 (2020), pp. 274-282.

Formula

Equals 5/2 - Pi^2/24 - zeta(3).

Example

0.88670958012834910548215804682704371193027623235780...

Mathematica

RealDigits[5/2 - Pi^2/24 - Zeta[3], 10, 100][[1]]

Crossrefs

Cf. A001008, A002805, A002117, A222171.

Sequence in context: A340168 A019704 A140976 * A253270 A021057 A335494

Adjacent sequences: A348369 A348370 A348371 * A348373 A348374 A348375

Keyword

nonn,cons

Author

Amiram Eldar, Oct 15 2021

Status

approved