A340485 Decimal expansion of Sum_{k>=2} log(k)/(k^2-1)^2.

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

Offset

0,3

Links

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

Formula

Equals -Sum_{i>=1} i*zeta'(2*i+2) = A261506 - Sum_{i>=2} i*zeta'(2*i+2).

Example

0.10732537164203023969506024850218288032472798982043615...

Maple

evalf(-Zeta'(4) - Sum(i * Zeta'(2*i+2), i = 2 .. infinity), 120); # Amiram Eldar, Mar 09 2024

Prog

(PARI) sumpos(k=2, log(k)/(k^2-1)^2) \\ Michel Marcus, Jan 09 2021
(PARI) -zeta'(4) - sumpos(i=2, i*zeta'(2*i+2)) \\ Amiram Eldar, Mar 09 2024

Crossrefs

Cf. A261506, A340440, A340484.

Sequence in context: A271353 A098907 A153205 * A309387 A298530 A243377

Adjacent sequences: A340482 A340483 A340484 * A340486 A340487 A340488

Keyword

nonn,cons

Author

R. J. Mathar, Jan 09 2021

Extensions

More terms from Amiram Eldar, Mar 09 2024

Status

approved