This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A299633 #7 Feb 16 2025 08:33:53 %S A299633 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 A299633 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 A299633 8,2,2,7,3,4,2,1,5,2,7,8,0,7,1,4,3,4 %N A299633 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 A299633 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 A299633 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a> %e A299633 e^(2*W(e/2)) = 3.9359563307913488100211988489777007... %t A299633 w[x_] := ProductLog[x]; x = e/2; y = e/2; N[E^(w[x] + w[y]), 130] (* A299633 *) %o A299633 (PARI) exp(2*lambertw(exp(1)/2)) \\ _Altug Alkan_, Mar 13 2018 %Y A299633 Cf. A299613, A299632. %K A299633 nonn,cons,easy %O A299633 1,1 %A A299633 _Clark Kimberling_, Mar 13 2018