A299629 - OEIS

%I #7 Mar 13 2018 22:10:30

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

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

%U 8,5,5,2,5,5,5,1,9,6,8,1,3,2,8,1,6,2

%N Decimal expansion of e^(2*W(1/3)) = (1/9)/(W(1/3))^2, where W is the Lambert W function (or PowerLog); see Comments.

%C The Lambert W function satisfies the functional equation e^(W(x) + W(y)) = x*y/(W(x)*W(y)) for x and y greater than -1/e, so that e^(2*W(1/3)) = (1/9)/(W(1/3))^2.  See A299613 for a guide to related constants.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>

%e e^(2*W(1/3)) = 1.674065846464880772226081114...

%t w[x_] := ProductLog[x]; x = 1/3; y = 1/3; N[E^(w[x] + w[y]), 130]   (* A299629 *)

%o (PARI) exp(2*lambertw(1/3)) \\ _Altug Alkan_, Mar 13 2018

%Y Cf. A299613, A299628.

%K nonn,cons,easy

%O 1,2

%A _Clark Kimberling_, Mar 13 2018