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Decimal expansion of e^(2*W(3/2)) = (9/4)/(W(3/2))^2, where W is the Lambert W function (or PowerLog); see Comments.
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%I #7 Mar 13 2018 22:10:53

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

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

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

%N Decimal expansion of e^(2*W(3/2)) = (9/4)/(W(3/2))^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(3/2)) = (9/4)/(W(3/2))^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(3/2)) = 4.2704649783213837050754449...

%t w[x_] := ProductLog[x]; x = 3/2; y = 3/2;

%t N[E^(w[x] + w[y]), 130] (* A299631 *)

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

%Y Cf. A299613, A299630.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Mar 13 2018