A240242 Decimal expansion of Integral_(x=1..c) (log(x)/(1+x))^2 dx, where c = A141251 = e^(LambertW(1/e)+1) corresponds to the maximum of the function.

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

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Jean-François Alcover, Graphics

Formula

A195055 = A013661 + A240242 + A240243.

(log(c)/(1+c))^2 = (LambertW(1/e))^2 = 0.0775425...

Example

0.13847532425848...

Mathematica

w = ProductLog[1/E]; Pi^2/6 - w - w^2 - 2*Log[1+w]*(1+w) + 2*PolyLog[2, -w] // RealDigits[#, 10, 100]& // First

Prog

(PARI) (w -> Pi^2/6 - w - w^2 - 2*(1+w)*log(1+w) + 2*polylog(2, -w))(lambertw(exp(-1))) \\ Charles R Greathouse IV, Aug 27 2014

Crossrefs

Cf. A013661, A141251, A195055, A240243.

Sequence in context: A021030 A276682 A303215 * A340782 A010628 A225456

Adjacent sequences: A240239 A240240 A240241 * A240243 A240244 A240245

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 03 2014

Status

approved