A397290 - OEIS

A397290

Decimal expansion of Sum_{k>=1} (-1)^(k+1) * AH(k,6)/k, where AH(k,6) = A136677(k)/A334605(k) is the k-th alternating harmonic (or skew-harmonic) number of order 6.

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

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OFFSET

0,1

LINKS

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

Cornel Ioan Vălean, More (Almost) Impossible Integrals, Sums, and Series, Springer Cham, 2023. See section 4.22, p. 427.

Index entries for sequences related to harmonic numbers.

FORMULA

Equals 505*zeta(7)/128 - 15*zeta(2)*zeta(5)/16 - 3*zeta(3)*zeta(4)/4 - log(2)*zeta(6).

EXAMPLE

0.6982510199799595210211402705965470491535381466488507...

MATHEMATICA

RealDigits[505*Zeta[7]/128 - 15*Zeta[2]*Zeta[5]/16 - 3*Zeta[3]*Zeta[4]/4 - Log[2]*Zeta[6], 10, 120][[1]]

PROG

(PARI) 505*zeta(7)/128 - 15*zeta(2)*zeta(5)/16 - 3*zeta(3)*zeta(4)/4 - log(2)*zeta(6)

CROSSREFS

Cf. A136677, A334605.

Cf. A002117, A002162, A013661, A013662, A013663, A013664, A013665.

Sum_{k>=1} (-1)^(k+1) * AH(k,m)/k: A369884 (m=1), A397288 (m=2), A397289 (m=4), this constant (m=6), A397291 (m=8).

Sequence in context: A119801 A191608 A266563 * A382197 A383955 A335028

Adjacent sequences: A397287 A397288 A397289 * A397291 A397292 A397293

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Jun 20 2026

STATUS

approved