A299631 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.

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

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(3/2)) = (9/4)/(W(3/2))^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(3/2)) = 4.2704649783213837050754449...

Mathematica

w[x_] := ProductLog[x]; x = 3/2; y = 3/2;
N[E^(w[x] + w[y]), 130]   (* A299631 *)

Prog

(PARI) exp(2*lambertw(3/2)) \\ Altug Alkan, Mar 13 2018

Crossrefs

Cf. A299613, A299630.

Sequence in context: A176385 A155829 A181051 * A205143 A266394 A353575

Adjacent sequences: A299628 A299629 A299630 * A299632 A299633 A299634

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 13 2018

Status

approved