A397200 Decimal expansion of Sum_{k>=1} AH(k)/k^3, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic (or skew-harmonic) number.

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

Offset

1,4

Links

Table of n, a(n) for n=1..106.

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 7*log(2)*zeta(3)/4 - 5*zeta(4)/16.

Example

1.119878107736230303681333271738615212197978105306143...

Mathematica

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

Prog

(PARI) 7*log(2)*zeta(3)/4 - 5*zeta(4)/16

Crossrefs

Cf. A058312, A058313.

Cf. A002117, A002162, A013661, A013662.

Sum_{k>=1} AH(k)/k^m: A397199 (m=2), this constant (m=3), A397201 (m=4).

Sequence in context: A369763 A347201 A021905 * A200688 A288239 A163243

Adjacent sequences: A397197 A397198 A397199 * A397201 A397202 A397203

Keyword

nonn,cons

Author

Amiram Eldar, Jun 18 2026

Status

approved