A395618 Decimal expansion of Sum_{k>=1} H(k)/((k+1)^2*2^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

Offset

0,2

Links

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

Michael I. Shamos, Shamos's Catalog of the Real Numbers, 2011.

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.51, p. 308, eq. (4.79), section 5.51, p. 326, section 6.51, pp. 498-502.

Index entries for sequences related to harmonic numbers.

Formula

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

Equals Integral_{x=0..1} log(1+x)^2/(x*(x+1)) dx = Integral_{x=1..2} log(x)^2/(x*(x-1)) dx (Shamos, 2011, p. 253).

Example

0.189506008460255411443650012840618982972537744635589...

Mathematica

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

Prog

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

Crossrefs

Cf. A001008, A002805.

Cf. A002117, A002162.

Sum_{k>=1} H(k)/((k+1)^m*2^k): A016627 (m=0), A253191 (m=1), this constant (m=2), A396733 (m=3), A396735 (m=4).

Sequence in context: A243267 A243268 A203071 * A394967 A091725 A029689

Adjacent sequences: A395614 A395615 A395617 * A395619 A395620 A395621

Keyword

nonn,cons,changed

Author

Amiram Eldar, Jun 04 2026

Status

approved