%I #23 Aug 17 2026 13:22:34

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

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

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

%N Decimal expansion of 1/(1+LambertW(1)).

%H G. C. Greubel, <a href="/A115287/b115287.txt">Table of n, a(n) for n = 0..10000</a>

%H Cristina B. Corcino, Roberto B. Corcino and István Mező, <a href="https://doi.org/10.1007/s00010-018-0559-2">Continued fraction expansions for the Lambert W function</a>, Aequationes mathematicae, Vol. 93, No. 2 (2019), pp. 485-49.

%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/45745/interesting-integral-related-to-the-omega-constant-lambert-w-function">Interesting integral related to the Omega Constant/Lambert W Function</a>, 2011.

%H Victor H. Moll, <a href="https://www.experimentalmath.info/maa-course/Moll-MAA.pdf">Some Questions in the Evaluation of Definite Integrals</a>, MAA Short Course, San Antonio, TX, January 2006.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OmegaConstant.html">Omega Constant</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DefiniteIntegral.html">Definite Integral</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals Integral_{x=-oo..oo} 1/(Pi^2 + (exp(x)-x)^2) dx (discovered by Victor Adamchik). - _Amiram Eldar_, Jul 04 2021

%e 0.63810374336511077852...

%t RealDigits[1/(1 + ProductLog[1]), 10, 105] // First (* _Jean-François Alcover_, Feb 07 2013 *)

%o (PARI) 1/(1 + lambertw(1)) \\ _G. C. Greubel_, Nov 05 2017

%Y Cf. A006153, A030178, A097172, A097173, A097174, A265953, A276231, A302399.

%K nonn,cons,easy

%O 0,1

%A _Eric W. Weisstein_, Jan 19 2006