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.

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, 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, 8, 2, 2, 7, 3, 4, 2, 1, 5, 2, 7, 8, 0, 7, 1, 4, 3, 4

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..86.

Eric Weisstein's World of Mathematics, Lambert W-Function

Example

e^(2*W(e/2)) = 3.9359563307913488100211988489777007...

Mathematica

w[x_] := ProductLog[x]; x = e/2; y = e/2; N[E^(w[x] + w[y]), 130]   (* A299633 *)

Prog

(PARI) exp(2*lambertw(exp(1)/2)) \\ Altug Alkan, Mar 13 2018

Crossrefs

Cf. A299613, A299632.

Sequence in context: A072560 A290506 A303111 * A074959 A010632 A340036

Adjacent sequences: A299630 A299631 A299632 * A299634 A299635 A299636

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 13 2018

Status

approved