A384461 Decimal expansion of Sum_{k>=1} H(k)^4/k^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

Offset: 2

Author

Amiram Eldar, May 30 2025

Keywords

• nonn
• cons
• easy

Examples

			45.83394146541655719259576578914226334887951133154848...
		

References

• Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2021, p. 230, eq. (4.122).

Links

• Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, p. 296, eq. (4.39).

Crossrefs

Cf. A001008, A002805.

Cf. A002117, A013664.

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

Programs

Mathematica

RealDigits[979*Zeta[6]/24 + 3*Zeta[3]^2, 10, 120][[1]]

PARI

979*zeta(6)/24 + 3*zeta(3)^2

Formula

Equals 979*zeta(6)/24 + 3*zeta(3)^2.