A395478 Decimal expansion of Sum_{k>=1} H(k)*H(k,2)/k^4, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number, and H(k,2) = A007406(k)/A007407(k) is the k-th generalized harmonic number of order 2.

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

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.42, pp. 301-302, eq. (4.58), section 5.42, p. 324, section 6.42, pp. 465-469.

Index entries for sequences related to harmonic numbers.

Formula

Equals 2*zeta(2)*zeta(5) + 3*zeta(3)*zeta(4)/4 - 51*zeta(7)/16.

Example

1.173002842836058301037904156231235020472776916429779...

Mathematica

RealDigits[2*Zeta[2]*Zeta[5] + 3*Zeta[3]*Zeta[4]/4 - 51*Zeta[7]/16, 10, 120][[1]]

Prog

(PARI) 2*zeta(2)*zeta(5) + 3*zeta(3)*zeta(4)/4 - 51*zeta(7)/16

Crossrefs

Cf. A001008, A002805.

Cf. A002117, A013661, A013662, A013663, A013665.

Sequence in context: A350621 A395608 A103237 * A338305 A239120 A369134

Adjacent sequences: A395475 A395476 A395477 * A395479 A395480 A395481

Keyword

nonn,cons

Author

Amiram Eldar, Jun 04 2026

Status

approved