A342361 Decimal expansion of 1/(omega+1)^2, where omega=1/LambertW(1).

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

Offset: 0

Author

Gleb Koloskov, Mar 09 2021

Keywords

• nonn
• cons

Examples

			0.1309689005663456008580754336956370484226429615564731843
		

Crossrefs

Cf. A342359, A342360, A030178, A030797.

Programs

Mathematica

Omega=LambertW[1]; xi=ArcTan[Sqrt[Omega]]; N[Sin[xi]^4,120]
omega=1/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]
RealDigits[1/(1/LambertW[1]+1)^2,10,120][[1]] (* Harvey P. Dale, Mar 26 2025 *)

PARI

my(Omega=lambertw(1), xi=atan(sqrt(Omega))); sin(xi)^4

PARI

1/(1/lambertw(1)+1)^2

Formula

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

Equals sin(A342359)^4 = 1/(A030797+1)^2 = (1-sqrt(A342360))^2.