A396733 - OEIS

%I #10 Jul 08 2026 14:54:02

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

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

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

%N Decimal expansion of Sum_{k>=1} H(k)/((k+1)^3*2^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

%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 4.51, p. 308, eq. (4.81), section 5.51, p. 326, section 6.51, pp. 498-502.

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

%F Equals (zeta(4) - log(2)*zeta(3) + log(2)^4/3)/4.

%e 0.081516478318618503841518434867219680679963460771833...

%t RealDigits[(Zeta[4] - Log[2]*Zeta[3] + Log[2]^4/3)/4, 10, 120][[1]]

%o (PARI) (zeta(4) - log(2)*zeta(3) + log(2)^4/3)/4

%Y Cf. A001008, A002805.

%Y Cf. A002117, A002162, A013662.

%Y Sum_{k>=1} H(k)/((k+1)^m*2^k): A016627 (m=0), A253191 (m=1), A395618 (m=2), this constant (m=3), A396735 (m=4).

%K nonn,cons,changed

%O 0,2

%A _Amiram Eldar_, Jun 04 2026

%E Data, formula and programs corrected by _Amiram Eldar_, Jul 08 2026