A349252 Decimal expansion of Sum_{k>=1} (-1)^k * log(k) / k^4.

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

Offset

0,2

Comments

First derivative of the Dirichlet eta function at 4.

Links

Table of n, a(n) for n=0..120.

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Formula

Equals (Pi^4 * log(2) + 630 * zeta'(4)) / 720.

Example

0.0334788045785650663859568547887377997137597304057...

Mathematica

Flatten[{0, RealDigits[(Pi^4 Log[2] + 630 Zeta'[4])/720, 10, 120][[1]]}]

Prog

(PARI) sumalt(k=1, (-1)^k * log(k) / k^4) \\ Michel Marcus, Nov 12 2021

Crossrefs

Cf. A013662, A091812, A210593, A256358, A261506, A267315, A349220.

Sequence in context: A051263 A378248 A058674 * A152651 A343396 A091973

Adjacent sequences: A349249 A349250 A349251 * A349253 A349254 A349255

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Nov 12 2021

Status

approved