A342360 Decimal expansion of 1/(Omega+1)^2, where Omega=LambertW(1) is the Omega constant.

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

Offset

0,1

Links

Table of n, a(n) for n=0..95.

Formula

Equals cos(A342359)^4 = 1/(A030178+1)^2 = (1-sqrt(A342361))^2.

Equals Integral_{t=0..1} (-t/LambertW(-1,-t*Omega^omega))^Omega, where omega=1/Omega=1/LambertW(1).

Equals A115287^2. - Vaclav Kotesovec, Mar 12 2021

Example

0.40717638729656715790289020473539767731...

Mathematica

Omega=LambertW[1]; xi=ArcTan[Sqrt[Omega]]; N[Cos[xi]^4, 120]
Omega=LambertW[1]; N[1/(Omega+1)^2, 120]
Omega=LambertW[1]; omega=1/Omega; NIntegrate[(-t/LambertW[-1, -t*Omega^omega])^Omega, {t, 0, 1}, WorkingPrecision->120]

Prog

(PARI) cos(atan(sqrt(lambertw(1))))^4
(PARI) my(Omega=lambertw(1)); 1/(Omega+1)^2

Crossrefs

Cf. A342359, A342361, A030178, A030797.

Sequence in context: A199071 A351898 A157698 * A251967 A330725 A057641

Adjacent sequences: A342357 A342358 A342359 * A342361 A342362 A342363

Keyword

nonn,cons

Author

Gleb Koloskov, Mar 09 2021

Status

approved