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%I #9 Mar 04 2018 04:09:22
%S 3,1,0,8,9,5,4,7,6,3,5,7,9,9,3,6,1,8,5,4,8,0,9,4,5,4,0,5,4,2,4,5,6,9,
%T 3,0,7,8,5,0,1,5,8,1,2,1,5,7,4,0,8,0,7,7,1,5,5,1,0,9,7,0,4,4,2,6,5,0,
%U 1,6,1,5,4,9,3,5,9,0,1,3,3,8,7,9,6,5
%N Decimal expansion of e^(2*A030178) = e^(2*W(1)) = (1/W(1))^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)) = (W(1))^(-2). See A299613 for a guide to related constants.
%H G. C. Greubel, <a href="/A299614/b299614.txt">Table of n, a(n) for n = 1..10000</a>
%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)) = 3.1089547635799361854809454054...
%t w[x_] := ProductLog[x]; x = 1; y = 1;
%t N[E^(w[x] + w[y]), 130] (* A299614 *)
%t RealDigits[(1/LambertW[1])^2, 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *)
%o (PARI) (1/lambertw(1))^2 \\ _G. C. Greubel_, Mar 03 2018
%Y Cf. A299613.
%K nonn,cons,easy
%O 1,1
%A _Clark Kimberling_, Mar 01 2018
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