A397532 - OEIS

%I #5 Jun 30 2026 09:16:36

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

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

%U 0,9,2,8,9,5,5,3,5,7,2,1,8,9,7,8,1,5,6,2,6,2,5,5,3,1,2,7,2,2,7,5,5,1,9,5,3

%N Decimal expansion of Sum_{k>=1} H(k,5)/k^2, where H(k,5) = A099828(k)/A069052(k) is the k-th generalized harmonic number of order 5.

%H Ali Shadhar Olaikhan, <a href="https://www.researchgate.net/publication/373488370">An Introduction to the Harmonic Series and Logarithmic Integrals</a>, 2nd ed., 2023, section 4.1.10, p. 267.

%H Cornel Ioan Vălean, <a href="https://doi.org/10.1007/978-3-030-02462-8">(Almost) Impossible Integrals, Sums, and Series</a>, Springer International Publishing, 2019, section 4.21, p. 292, section 5.21, p. 319, section 6.21, pp. 384-392, eq. (6.76).

%H <a href="/index/Ha#harmonic">Index entries for sequences related to harmonic numbers</a>.

%F Equals 11*zeta(7) - 4*zeta(2)*zeta(5) - 2*zeta(3)*zeta(4).

%e 1.667102664953032184981049768484422186704299260403309...

%t RealDigits[11*Zeta[7] - 4*Zeta[2]*Zeta[5] - 2*Zeta[3]*Zeta[4], 10, 120][[1]]

%o (PARI) 11*zeta(7) - 4*zeta(2)*zeta(5) - 2*zeta(3)*zeta(4)

%Y Cf. A069052, A099828.

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

%K nonn,cons

%O 1,2

%A _Amiram Eldar_, Jun 30 2026