A382846 Decimal expansion of 4 - Pi^2/4 - 2*log(2).

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

Offset

0,2

Links

Table of n, a(n) for n=0..86.

I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products (6th ed.), 2000, (eq. 0.236.7).

Formula

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

Equals Integral_{x=0..1} log(x)*log(1-x^2) dx. - Amiram Eldar, Aug 08 2025

Example

0.1463045386077697264569...

Mathematica

RealDigits[4 - Pi^2/4 - 2*Log[2], 10, 120][[1]] (* Amiram Eldar, Aug 08 2025 *)

Crossrefs

Cf. A016627, A091476.

Sequence in context: A212084 A182368 A185442 * A204174 A086467 A197731

Adjacent sequences: A382843 A382844 A382845 * A382847 A382848 A382849

Keyword

nonn,cons

Author

Sean A. Irvine, Apr 06 2025

Status

approved