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%I #6 Mar 13 2018 22:10:41
%S 3,9,3,5,9,5,6,3,3,0,7,9,1,3,4,8,8,1,0,0,2,1,1,9,8,8,4,8,9,7,7,7,0,0,
%T 7,1,8,2,9,0,2,6,6,4,3,5,6,9,6,1,5,7,6,1,0,7,4,6,1,1,8,7,0,6,0,4,2,6,
%U 8,2,2,7,3,4,2,1,5,2,7,8,0,7,1,4,3,4
%N Decimal expansion of e^(2*W(e/2)) = (e^2/4)/(W(e/2))^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(e/2)) = (e^2/4)/(W(e/2))^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(e/2)) = 3.9359563307913488100211988489777007...
%t w[x_] := ProductLog[x]; x = e/2; y = e/2; N[E^(w[x] + w[y]), 130] (* A299633 *)
%o (PARI) exp(2*lambertw(exp(1)/2)) \\ _Altug Alkan_, Mar 13 2018
%Y Cf. A299613, A299632.
%K nonn,cons,easy
%O 1,1
%A _Clark Kimberling_, Mar 13 2018