Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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