A329117 Decimal expansion of Sum_{k>=1} (k^(1/k^2) - 1).

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

Offset

0,1

Links

Table of n, a(n) for n=0..84.

Formula

Equals Sum_{k>=1} (-1)^k / k! * k-th derivative of zeta(2*k). - Vaclav Kotesovec, Jun 18 2023

Example

0.971499034283308757222625062314754580022...

Mathematica

digits = 120; d = 1; j = 2; s = Pi^2 * (2*Log[Glaisher] - Log[2*Pi]/6 - EulerGamma/6); While[Abs[d] > 10^(-digits - 5), d = (-1)^j/j!*Derivative[j][Zeta][2*j]; s += d; j++]; RealDigits[s, 10, 120][[1]] (* Vaclav Kotesovec, Jun 18 2023 *)

Prog

(PARI) sumpos(k=1, k^(1/k^2) - 1) \\ Michel Marcus, Nov 05 2019

Crossrefs

Cf. A073002, A098572.

Sequence in context: A155691 A106727 A094134 * A309570 A254249 A298752

Adjacent sequences: A329114 A329115 A329116 * A329118 A329119 A329120

Keyword

nonn,cons

Author

Daniel Hoyt, Nov 05 2019

Status

approved