cp's OEIS Frontend

A384461 Decimal expansion of Sum_{k>=1} H(k)^4/k^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

%I A384461 #5 May 30 2025 10:35:10
%S A384461 4,5,8,3,3,9,4,1,4,6,5,4,1,6,5,5,7,1,9,2,5,9,5,7,6,5,7,8,9,1,4,2,2,6,
%T A384461 3,3,4,8,8,7,9,5,1,1,3,3,1,5,4,8,4,8,4,2,3,2,5,4,9,2,2,2,5,7,1,5,3,9,
%U A384461 1,3,5,1,9,5,9,3,6,4,2,8,2,2,3,7,0,0,0,6,7,8,1,2,2,9,8,2,9,9,6,0,6,5,2,7,4
%N A384461 Decimal expansion of Sum_{k>=1} H(k)^4/k^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
%D A384461 Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2021, p. 230, eq. (4.122).
%H A384461 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, p. 296, eq. (4.39).
%F A384461 Equals 979*zeta(6)/24 + 3*zeta(3)^2.
%e A384461 45.83394146541655719259576578914226334887951133154848...
%t A384461 RealDigits[979*Zeta[6]/24 + 3*Zeta[3]^2, 10, 120][[1]]
%o A384461 (PARI) 979*zeta(6)/24 + 3*zeta(3)^2
%Y A384461 Cf. A001008, A002805.
%Y A384461 Cf. A002117, A013664.
%Y A384461 Related constants: A152648, A152649, A152651, A218505, A233090, A238168, A238181, A238182, A241753, A244667, A253191, A256988, A345203.
%K A384461 nonn,cons,easy
%O A384461 2,1
%A A384461 _Amiram Eldar_, May 30 2025