A396733 Decimal expansion of Sum_{k>=1} H(k)/((k+1)^3*2^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

Offset

0,2

Links

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

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.51, p. 308, eq. (4.81), section 5.51, p. 326, section 6.51, pp. 498-502.

Index entries for sequences related to harmonic numbers.

Formula

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

Example

0.081516478318618503841518434867219680679963460771833...

Mathematica

RealDigits[(Zeta[4] - Log[2]*Zeta[3] + Log[2]^4/3)/4, 10, 120][[1]]

Prog

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

Crossrefs

Cf. A001008, A002805.

Cf. A002117, A002162, A013662.

Sum_{k>=1} H(k)/((k+1)^m*2^k): A016627 (m=0), A253191 (m=1), A395618 (m=2), this constant (m=3), A396735 (m=4).

Sequence in context: A280040 A202284 A231772 * A338935 A393259 A200120

Adjacent sequences: A396725 A396726 A396727 * A396734 A396735 A396736

Keyword

nonn,cons,changed

Author

Amiram Eldar, Jun 04 2026

Extensions

Data, formula and programs corrected by Amiram Eldar, Jul 08 2026

Status

approved