A342360 - OEIS

%I #14 Apr 04 2021 01:11:13

%S 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,

%T 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,

%U 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

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

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

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

%F Equals A115287^2. - _Vaclav Kotesovec_, Mar 12 2021

%e 0.40717638729656715790289020473539767731...

%t Omega=LambertW[1]; xi=ArcTan[Sqrt[Omega]]; N[Cos[xi]^4,120]

%t Omega=LambertW[1]; N[1/(Omega+1)^2,120]

%t Omega=LambertW[1]; omega=1/Omega; NIntegrate[(-t/LambertW[-1,-t*Omega^omega])^Omega,{t,0,1}, WorkingPrecision->120]

%o (PARI) cos(atan(sqrt(lambertw(1))))^4

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

%Y Cf. A342359, A342361, A030178, A030797.

%K nonn,cons

%O 0,1

%A _Gleb Koloskov_, Mar 09 2021