A397636 Decimal expansion of Sum_{k>=1} H(k)^3*H(k,2)/k^2, 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, 8, 5, 3, 0, 3, 0, 7, 9, 4, 9, 3, 6, 7, 8, 5, 6, 8, 1, 4, 0, 9, 8, 5, 6, 2, 5, 5, 9, 6, 2, 9, 5, 5, 6, 5, 0, 7, 1, 0, 1, 1, 3, 5, 5, 7, 2, 6, 6, 3, 3, 8, 0, 5, 5, 0, 9, 8, 5, 6, 8, 9, 0, 7, 8, 6, 7, 6, 5, 7, 5, 8, 9, 3, 1, 4, 8, 0, 1, 5, 5, 2, 9, 1, 3, 1, 2, 2, 8, 7, 4, 5, 6, 6, 4, 9, 7, 8, 6, 0, 2, 1, 0, 9, 7

Offset

2,2

Links

Table of n, a(n) for n=2..106.

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.43, pp. 302-303, eq. (4.66), section 5.43, p. 324, section 6.43, pp. 470-479.

Index entries for sequences related to harmonic numbers.

Formula

Equals 83*zeta(7)/16 - 5*zeta(2)*zeta(5)/2 + 27*zeta(3)*zeta(4)/2.

Example

18.53030794936785681409856255962955650710113557266338...

Mathematica

RealDigits[83*Zeta[7]/16 - 5*Zeta[2]*Zeta[5]/2 + 27*Zeta[3]*Zeta[4]/2, 10, 120][[1]]

Prog

(PARI) 83*zeta(7)/16 - 5*zeta(2)*zeta(5)/2 + 27*zeta(3)*zeta(4)/2

Crossrefs

Cf. A001008, A002805, A007406, A007407.

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

Sequence in context: A198918 A196515 A116397 * A275306 A176705 A140133

Adjacent sequences: A397633 A397634 A397635 * A397637 A397638 A397640

Keyword

nonn,cons,new

Author

Amiram Eldar, Jul 03 2026

Status

approved