A394397 Decimal expansion of Sum_{k>=1} H(k)*H(k,3)/k^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number, and H(k,3) = A007408(k)/A007409(k) is the k-th generalized harmonic number of order 3.

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

Offset

1,1

References

Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2021, p. 227, eq. (4.118).

Links

Table of n, a(n) for n=1..105.

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.29, p. 295, eq. (4.37), section 5.29, p. 321, section 6.29, pp. 414-421.

Index entries for sequences related to harmonic numbers.

Formula

Equals (227*zeta(6)/24 - 3*zeta(3)^2)/2.

Example

2.643773699651006039029380091425746589093408771301203...

Mathematica

RealDigits[(227*Zeta[6]/24 - 3*Zeta[3]^2)/2, 10, 120][[1]]

Prog

(PARI) (227*zeta(6)/24 - 3*zeta(3)^2)/2

Crossrefs

Cf. A001008, A002805, A007408, A007409.

Cf. A002117, A013664.

Sequence in context: A385261 A003571 A068457 * A299402 A286451 A102510

Adjacent sequences: A394394 A394395 A394396 * A394398 A394399 A394400

Keyword

nonn,cons,changed

Author

Amiram Eldar, Jun 04 2026

Status

approved