A379425 Decimal expansion of Ni_2 = gamma/3 - log(2*Pi)/2 - 2*zeta'(-1) + 2/3, where gamma = A001620.

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Marc-Antoine Coppo, A note on some alternating series involving zeta and multiple zeta values, Journal of Mathematical Analysis and Applications Volume 475, Issue 2, 15 July 2019, Pages 1831-1841.

Formula

Equals Sum_{s>=2} (-1)^(s)*zeta(s)/(s+2).

Equals A001620/3 - log(2*A000796)/2 + 2*log(A074962) + 1/2.

Example

0.270975642496740070183013614107411122680728399012594687451148817...

Mathematica

RealDigits[EulerGamma/3 - Log[2 Pi]/2 + 2/3 - 2 Zeta'[-1], 10, 105][[1]]

Crossrefs

Cf. A000796, A001620, A074962, A131688 (Ni_-1), A321943 (Ni_1), A379751 (Ni_3).

Sequence in context: A016638 A199398 A296453 * A081544 A011294 A282072

Adjacent sequences: A379420 A379423 A379424 * A379426 A379427 A379428

Keyword

cons,nonn

Author

Artur Jasinski, Dec 22 2024

Status

approved