This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342361 #12 Mar 26 2025 10:35:59
%S A342361 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 A342361 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 A342361 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 A342361 Decimal expansion of 1/(omega+1)^2, where omega=1/LambertW(1).
%F A342361 Equals Integral_{t=0..1} (-t/W(-1,-t*Omega^omega))^omega, where omega = 1/Omega = 1/LambertW(1).
%F A342361 Equals sin(A342359)^4 = 1/(A030797+1)^2 = (1-sqrt(A342360))^2.
%e A342361 0.1309689005663456008580754336956370484226429615564731843
%t A342361 Omega=LambertW[1]; xi=ArcTan[Sqrt[Omega]]; N[Sin[xi]^4,120]
%t A342361 omega=1/LambertW[1]; N[1/(omega+1)^2,120]
%t A342361 Omega=LambertW[1]; omega=1/Omega; NIntegrate[(-t/LambertW[-1,-t*Omega^omega])^omega,{t,0,1}, WorkingPrecision->120]
%t A342361 RealDigits[1/(1/LambertW[1]+1)^2,10,120][[1]] (* _Harvey P. Dale_, Mar 26 2025 *)
%o A342361 (PARI) my(Omega=lambertw(1), xi=atan(sqrt(Omega))); sin(xi)^4
%o A342361 (PARI) 1/(1/lambertw(1)+1)^2
%Y A342361 Cf. A342359, A342360, A030178, A030797.
%K A342361 nonn,cons
%O A342361 0,2
%A A342361 _Gleb Koloskov_, Mar 09 2021