A300916 Decimal expansion of the first derivative of the infinite power tower function x^x^x... at x = 1/e.

5, 5, 7, 9, 1, 9, 2, 8, 2, 2, 5, 5, 4, 1, 6, 0, 4, 6, 7, 7, 3, 8, 6, 4, 7, 3, 3, 1, 3, 7, 2, 8, 4, 3, 2, 5, 2, 6, 8, 0, 5, 9, 5, 2, 2, 1, 4, 7, 0, 0, 0, 5, 6, 8, 8, 5, 6, 8, 6, 1, 6, 7, 8, 6, 6, 5, 6, 6, 9, 1, 6, 8, 0, 8, 0, 0, 6, 2, 9, 0, 4, 7, 4, 3, 6, 9, 7, 5, 4, 6, 6, 9, 3, 4, 2, 8, 0, 5, 7, 8, 8, 8, 4, 1, 8, 2

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Power Tower

Wikipedia, Tetration

Formula

Equals exp(1)*exp(-2*LambertW(1))/(1+LambertW(1)).

Example

0.557919282255416046773864733137284325268059522147000568856861678665669168...

Mathematica

RealDigits[E*Exp[-2*LambertW[1]]/(1+LambertW[1]), 10, 100][[1]] (* G. C. Greubel, Sep 09 2018 *)

Prog

(PARI) exp(1)*exp(-2*lambertw(1))/(1+lambertw(1)) \\ Michel Marcus, Mar 16 2018

Crossrefs

Cf. A001113, A030178, A068985, A277522, A277651, A293009.

Sequence in context: A196348 A196351 A154583 * A134125 A097996 A033300

Adjacent sequences: A300913 A300914 A300915 * A300917 A300918 A300919

Keyword

nonn,cons

Author

Alois P. Heinz, Mar 16 2018

Status

approved