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

Author

Amiram Eldar, Oct 15 2021

Keywords

• nonn
• cons

Examples

			0.88670958012834910548215804682704371193027623235780...
		

Links

• 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.

Crossrefs

Cf. A001008, A002805, A002117, A222171.

Programs

Mathematica

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

Formula

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