A346962 Decimal expansion of Integral_{x=-1/e..0} LambertW(x)/LambertW(-1,x) dx.

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

Offset

0,2

Links

Table of n, a(n) for n=0..107.

Formula

Equals (1/e) + Integral_{x=0..1} log(x)*x^(1/(1-x))/(1-x) dx.

Equals (1/e) - Sum_{n>0} n^(n-2)/(n+1)^(n+1) = A068985-Sum_{n>0} A000272(n)/A000312(n+1).

Example

0.0556295897289868954612901466941050684561294869117252169349398695712429...

Maple

evalf(Integrate(LambertW(x)/LambertW(-1, x), x = -exp(-1)..0), 120); # Vaclav Kotesovec, Aug 23 2021

Mathematica

N[Integrate[LambertW[x]/LambertW[-1, x], {x, -1/E, 0}], 120]

Prog

(PARI) exp(-1)+intnum(x=0, 1, log(x)*x^(1/(1-x))/(1-x))

Crossrefs

Cf. A000272, A000312, A068985, A346963.

Sequence in context: A224093 A193555 A161981 * A258072 A091284 A276860

Adjacent sequences: A346959 A346960 A346961 * A346963 A346964 A346965

Keyword

nonn,cons

Author

Gleb Koloskov, Aug 09 2021

Status

approved