The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #5 Jun 30 2026 09:16:26
%S 1,0,9,3,5,0,9,0,9,9,9,1,6,7,5,6,4,7,8,2,4,6,6,0,3,5,6,8,7,2,2,1,6,4,
%T 1,0,5,5,5,7,2,0,3,0,6,9,1,5,2,1,1,6,0,2,6,8,8,4,3,8,6,5,6,8,6,2,4,9,
%U 1,0,0,5,5,0,6,8,2,2,7,5,0,1,8,5,7,2,7,0,3,5,5,6,7,2,0,3,6,3,4,4,6,8,9,5,0,2
%N Decimal expansion of Sum_{k>=1} H(k,3)/k^4, where H(k,3) = A007408(k)/A007409(k) is the k-th generalized harmonic number of order 3.
%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 4.2.21, p. 301, eq. (4.71).
%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. (6.80).
%H <a href="/index/Ha#harmonic">Index entries for sequences related to harmonic numbers</a>.
%F Equals 18*zeta(7) - 10*zeta(2)*zeta(5).
%e 1.093509099916756478246603568722164105557203069152116...
%t RealDigits[18*Zeta[7] - 10*Zeta[2]*Zeta[5], 10, 120][[1]]
%o (PARI) 18*zeta(7) - 10*zeta(2)*zeta(5)
%Y Cf. A007408, A007409.
%Y Cf. A013661, A013663, A013665.
%K nonn,cons,new
%O 1,3
%A _Amiram Eldar_, Jun 30 2026