A397631 Decimal expansion of Sum_{k>=1} H(k)*H(k,4)/k^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number, and H(k,4) = A007410(k)/A007480(k) is the k-th harmonic number of order 4.

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

Offset

1,1

Links

Table of n, a(n) for n=1..106.

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, section 4.43, pp. 302-303, eq. (4.60), section 5.43, p. 324, section 6.43, pp. 470-479.

Index entries for sequences related to harmonic numbers.

Formula

Equals 9*zeta(2)*zeta(5)/2 - 3*zeta(3)*zeta(4)/2 - 51*zeta(7)/16.

Example

2.509915558377422610407917096386899377535040737104199...

Mathematica

RealDigits[9*Zeta[2]*Zeta[5]/2 - 3*Zeta[3]*Zeta[4]/2 - 51*Zeta[7]/16, 10, 120][[1]]

Prog

(PARI) 9*zeta(2)*zeta(5)/2 - 3*zeta(3)*zeta(4)/2 - 51*zeta(7)/16

Crossrefs

Cf. A001008, A002805, A007410, A007480.

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

Sequence in context: A201745 A192042 A388495 * A391953 A214119 A088307

Adjacent sequences: A397628 A397629 A397630 * A397632 A397633 A397634

Keyword

nonn,cons,new

Author

Amiram Eldar, Jul 03 2026

Status

approved