A299625 Decimal expansion of e^(2*W(2)) = 4/(W(2))^2, where W is the Lambert W function (or PowerLog); see Comments.

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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(2)) = 4/(W(2))^2. See A299613 for a guide to related constants.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

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

Example

e^(2*W(2)) = 5.50254660422072407531126813594932...

Mathematica

w[x_] := ProductLog[x]; x = 2; y = 2;
N[E^(w[x] + w[y]), 130]   (* A299625 *)
RealDigits[(2/LambertW[2])^2, 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

(PARI) (2/lambertw(2))^2 \\ G. C. Greubel, Mar 03 2018

Crossrefs

Cf. A299613, A299624.

Sequence in context: A176144 A308356 A065936 * A021649 A357715 A200257

Adjacent sequences: A299622 A299623 A299624 * A299626 A299627 A299628

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 03 2018

Status

approved