A397661 - OEIS

%I #6 Jul 04 2026 10:07:09

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

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

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

%N Decimal expansion of Sum_{k>=1} (zeta(3) - H(k,3)) * H(k)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number, and H(k,3) = A007408(k)/A007409(k) is the k-th generalized harmonic number of order 3.

%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 4.44, pp. 303, eq. (4.69), section 5.44, p. 325, section 6.44, pp. 479-481.

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

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

%e 0.325361557592797494234391680370631555964519715063573...

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

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

%Y Cf. A001008, A002805, A007408, A007409.

%Y Cf. A002117, A013661, A013663.

%Y Sum_{k>=1} (zeta(m) - H(k,m)) * H(k)/k: A244664 (m=2), this constant (m=3), A397662 (m=4), A397663 (m=5).

%K nonn,cons,new

%O 0,1

%A _Amiram Eldar_, Jul 04 2026