A397375 Decimal expansion of Sum_{k>=1} (zeta(2) - H(k,2))*H(k)/(2*k+1), 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.

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

Offset

0,1

Links

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

Cornel Ioan Vălean, More (Almost) Impossible Integrals, Sums, and Series, Springer Cham, 2023. See section 4.29, p. 431, eq. (4.120), section 5.29, p. 463, section 6.29, pp. 646-651.

Index entries for sequences related to harmonic numbers.

Formula

Equals log(2)^4/6 - log(2)^2*zeta(2) - zeta(4)/2 + 4*Li_4(1/2).

Example

0.776913616156587749440029749938859188817810502311313...

Mathematica

RealDigits[Log[2]^4/6 - Log[2]^2*Zeta[2] - Zeta[4]/2 + 4*PolyLog[4, 1/2], 10, 120][[1]]

Prog

(PARI) log(2)^4/6 - log(2)^2*zeta(2) - zeta(4)/2 + 4*polylog(4, 1/2)

Crossrefs

Cf. A001008, A002805, A007406, A007407.

Cf. A002162, A013661, A013662, A099218.

Cf. A397376, A397377, A397378.

Sequence in context: A124930 A195202 A252799 * A382587 A022619 A393899

Adjacent sequences: A397372 A397373 A397374 * A397376 A397377 A397378

Keyword

nonn,cons

Author

Amiram Eldar, Jun 23 2026

Status

approved