A389748 Decimal expansion of Sum_{k>=2} zeta(k)/(k*(k+1)*2^k).

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

Offset

0,2

References

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, p. 324, eq. (569).

Links

Table of n, a(n) for n=0..105.

Junesang Choi, The Catalan's constant and series involving the zeta function, Communications of the Korean Mathematical Society, Vol. 13, No. 2 (1998), pp. 435-443. See p. 437, eq. (1.13).

Junesang Choi and H. M. Srivastava, Sums associated with the Zeta function, J. Math. Anal. Appl., Vol. 206, No. 1 (1997), pp. 103-120. See p. 109, eq. (2.23).

Formula

Equals -gamma/4 + 7*log(2)/12 + log(Pi)/2 - 3*log(A), where gamma is Euler's constant (A001620), and A is the Glaisher-Kinkelin constant (A074962).

Example

0.086133450924598848105045409944856484481706843177218...

Mathematica

RealDigits[-EulerGamma/4 + 7*Log[2]/12 + Log[Pi]/2 - 3*Log[Glaisher], 10, 120, -1][[1]]

Prog

(PARI) -Euler/4 + 7*log(2)/12 + log(Pi)/2 - 3/12 + 3*zeta'(-1)

Crossrefs

Cf. A001620, A002162, A053510, A074962, A225746.

Related constants: A389746, A389747.

Sequence in context: A372268 A011009 A394965 * A155184 A153101 A281822

Adjacent sequences: A389745 A389746 A389747 * A389749 A389750 A389751

Keyword

nonn,cons

Author

Amiram Eldar, Oct 13 2025

Status

approved