A384460 Decimal expansion of Sum_{k>=1} (-1)^(k+1)*H(k)^2/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

Offset: 0

Author

Amiram Eldar, May 30 2025

Keywords

• nonn
• cons
• easy

Examples

			0.44246018937791249521879821917465633518413362702258...
		

References

• Ovidiu Furdui, Limits, Series, and Fractional Part Integrals, Springer, 2013, section 3.4, p. 148.

Crossrefs

Cf. A001008, A002805.

Cf. A000796, A002117, A002162.

Related constants: A152648, A152649, A152651, A218505, A233090, A238168, A238181, A238182, A241753, A244667, A253191, A256988, A345203.

Programs

Mathematica

RealDigits[(9*Zeta[3] + 4*Log[2]^3 - Pi^2*Log[2])/12, 10, 120][[1]]

PARI

(9*zeta(3) + 4*log(2)^3 - Pi^2*log(2))/12

Formula

Equals (9*zeta(3) + 4*log(2)^3 - Pi^2*log(2))/12.