A389747 Decimal expansion of Sum_{k>=1} zeta(2*k+1)/((k+1)*(2*k+1)*(2*k+3)*4^k).

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

Offset

0,4

References

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, p. 330, eq. (607).

Links

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

Junesang Choi and Hari M. Srivastava, An experimental conjecture involving closed-form evaluation of series associated with the Zeta functions, Mathematical Inequalities & Applications, Vol. 16, No. 4 (2013), pp. 971-979. See p. 978, eq. (2.18).

Formula

Equals 3/2 - gamma/3 + log(2) - 8*log(A), where gamma is Euler's constant (A001620), and A is the Glaisher-Kinkelin constant (A074962).

Example

0.010706142655826922170370809488463948949155979698666...

Mathematica

RealDigits[3/2 - EulerGamma/3 + Log[2] - 8*Log[Glaisher], 10, 120, -1][[1]]

Prog

(PARI) 5/6 - Euler/3 + log(2) + 8*zeta'(-1)

Crossrefs

Cf. A001620, A002162, A074962, A225746.

Related constants: A389746, A389748.

Sequence in context: A362149 A195484 A130203 * A398128 A328717 A011479

Adjacent sequences: A389744 A389745 A389746 * A389748 A389749 A389750

Keyword

nonn,cons

Author

Amiram Eldar, Oct 13 2025

Status

approved