A397199 Decimal expansion of Sum_{k>=1} AH(k)/k^2, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic (or skew-harmonic) number.

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

Offset

1,2

Links

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

Cornel Ioan Vălean, More (Almost) Impossible Integrals, Sums, and Series, Springer Cham, 2023. See section 4.22, p. 425.

Index entries for sequences related to harmonic numbers.

Formula

Equals 3*log(2)*zeta(2)/2 - zeta(3)/4.

Example

1.409757890174380564861935248110661520133698188961853...

Mathematica

RealDigits[3*Log[2]*Zeta[2]/2 - Zeta[3]/4, 10, 120][[1]]

Prog

(PARI) 3*log(2)*zeta(2)/2 - zeta(3)/4

Crossrefs

Cf. A058312, A058313.

Cf. A002117, A002162, A013661.

Sum_{k>=1} AH(k)/k^m: this constant (m=2), A397200 (m=3), A397201 (m=4).

Sequence in context: A198866 A269720 A245638 * A176220 A197285 A357017

Adjacent sequences: A397196 A397197 A397198 * A397200 A397201 A397202

Keyword

nonn,cons

Author

Amiram Eldar, Jun 18 2026

Status

approved