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

Author

Gleb Koloskov, Mar 09 2021

Keywords

• nonn
• cons

Examples

			0.40717638729656715790289020473539767731...
		

Crossrefs

Cf. A342359, A342361, A030178, A030797.

Programs

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]

PARI

cos(atan(sqrt(lambertw(1))))^4

PARI

my(Omega=lambertw(1)); 1/(Omega+1)^2

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