A342361 - OEIS

%I #10 Apr 04 2021 01:11:41

%S 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,

%T 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,

%U 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

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

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

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

%e 0.1309689005663456008580754336956370484226429615564731843

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

%t omega=1/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) my(Omega=lambertw(1), xi=atan(sqrt(Omega))); sin(xi)^4

%o (PARI) 1/(1/lambertw(1)+1)^2

%Y Cf. A342359, A342360, A030178, A030797.

%K nonn,cons

%O 0,2

%A _Gleb Koloskov_, Mar 09 2021