A397026 Decimal expansion of Sum_{k>=1} H(k,2)/(2*k*(2*k+1)), where H(k,2) = A007406(k)/A007407(k) is the k-th generalized harmonic number of order 2.

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

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 4.15, p. 414, eq.(4.88), section 5.15, p. 460, and section 6.15, pp. 572-582.

Index entries for sequences related to harmonic numbers.

Formula

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

Example

0.362389718306640099275092842896963143239603024060971...

Mathematica

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

Prog

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

Crossrefs

Cf. A007406, A007407.

Cf. A002117, A002162, A013661.

Sequence in context: A021280 A282728 A193537 * A319674 A372696 A021738

Adjacent sequences: A397023 A397024 A397025 * A397027 A397028 A397029

Keyword

nonn,cons

Author

Amiram Eldar, Jun 14 2026

Status

approved