A350761 Decimal expansion of Pi^2*log(2)/6 - log(2)^3/3 - 3*zeta(3)/4.

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

Offset

0,2

Links

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

Ovidiu Furdui, Problem H-761, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 52, No. 4 (2014), p. 374; A Series Whose Sum Involves Pi, ln 2 and zeta(3), Solution to Problem H-761 by AN-anduud Problem Solving Group, ibid., Vol. 54, No. 3 (2016), pp. 283-285.

Formula

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

Example

0.12763051594351388351849171032151833742418129365974...

Mathematica

RealDigits[Pi^2*Log[2]/6 - Log[2]^3/3 - 3*Zeta[3]/4, 10, 100][[1]]

Crossrefs

Cf. A000796, A002117, A002162, A013661, A197070.

Sequence in context: A264692 A021366 A334366 * A135155 A308705 A244847

Adjacent sequences: A350758 A350759 A350760 * A350762 A350763 A350764

Keyword

nonn,cons

Author

Amiram Eldar, Jan 14 2022

Status

approved