A379751 Decimal expansion of Ni_3 = gamma/4 - log(2*Pi)/2 - 3*zeta'(-1) + 3*zeta'(-2) + 7/12, where gamma = A001620.

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

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+3).

Mathematica

RealDigits[EulerGamma/4 - Log[2 Pi]/2 - 3 Zeta'[-1] + 3 Zeta'[-2] + 7/12, 10, 105][[1]]

Crossrefs

Cf. A000796, A001620, A074962, A131688 (Ni_-1), A321943 (Ni_1), A379425 (Ni_2).

Sequence in context: A337407 A156914 A289656 * A248686 A059434 A292222

Adjacent sequences: A379747 A379748 A379749 * A379752 A379753 A379754

Keyword

cons,nonn

Author

Artur Jasinski, Jan 01 2025

Status

approved