A397661 Decimal expansion of Sum_{k>=1} (zeta(3) - H(k,3)) * H(k)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number, and H(k,3) = A007408(k)/A007409(k) is the k-th generalized harmonic number of order 3.

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

Offset

0,1

Links

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

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.44, pp. 303, eq. (4.69), section 5.44, p. 325, section 6.44, pp. 479-481.

Index entries for sequences related to harmonic numbers.

Formula

Equals 2*zeta(2)*zeta(3) - 7*zeta(5)/2.

Example

0.325361557592797494234391680370631555964519715063573...

Mathematica

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

Prog

(PARI) 2*zeta(2)*zeta(3) - 7*zeta(5)/2

Crossrefs

Cf. A001008, A002805, A007408, A007409.

Cf. A002117, A013661, A013663.

Sum_{k>=1} (zeta(m) - H(k,m)) * H(k)/k: A244664 (m=2), this constant (m=3), A397662 (m=4), A397663 (m=5).

Sequence in context: A057958 A225411 A247815 * A057953 A372679 A129231

Adjacent sequences: A397656 A397658 A397660 * A397662 A397663 A397666

Keyword

nonn,cons,new

Author

Amiram Eldar, Jul 04 2026

Status

approved