A397009 Decimal expansion of Sum_{k>=1} (-1)^(k+1)*H(k)/k^6, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

Offset

0,1

Links

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

Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2nd ed., 2023, p. 260.

Cornel Ioan Vălean, More (Almost) Impossible Integrals, Sums, and Series, Springer Cham, 2023. See section 4.21, pp. 421-422, section 5.21, p. 461, and section 6.21, pp. 608-615.

Index entries for sequences related to harmonic numbers.

Formula

Equals 377*zeta(7)/128 - 7*zeta(3)*zeta(4)/8 - zeta(2)*zeta(5)/2.

Example

0.978677486175124353297993827173539515522803312061313...

Mathematica

RealDigits[377*Zeta[7]/128 - 7*Zeta[3]*Zeta[4]/8 - Zeta[2]*Zeta[5]/2, 10, 120][[1]]

Prog

(PARI) 377*zeta(7)/128 - 7*zeta(3)*zeta(4)/8 - zeta(2)*zeta(5)/2

Crossrefs

Cf. A001008, A002805.

Cf. A002117, A013661, A013662, A013663, A013665.

Sum_{k>=1} (-1)^(k+1)*H(k)/k^m: A076788 (m=1), A233090 (m=2), A233033 (m=3), A396737 (m=4), this constant (m=6), A397010 (m=8), A397011 (m=10).

Sequence in context: A154827 A258942 A378967 * A249601 A298524 A212005

Adjacent sequences: A397006 A397007 A397008 * A397010 A397011 A397013

Keyword

nonn,cons

Author

Amiram Eldar, Jun 13 2026

Status

approved