A346963 Decimal expansion of Integral_{x=-1/e..0} LambertW(x)*LambertW(-1,x) dx.

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Formula

Equals Integral_{x=-1/e..0} LambertW(x)*LambertW(-1,x) dx.

Equals (3/e) - 1 + Sum_{n>0} (n^(n-1)/(n+1)^(n+2))*(Gamma(n+2,n+1)/Gamma(n+2)).

Equals (11/e)-4+Sum_{n>0} n^(n-1)/(n+1)^(n+2) = A135011-4+Sum_{n>0} A000169(n)/A007778(n+1).

Example

0.216577770436007277359024920060738331698735582255355693272331441694...

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) 11*exp(-1)-4+sumpos(n=1, (1/(1+1./n))^n/(n*(n+1)^2))

Crossrefs

Cf. A000169, A007778, A068985, A135003, A135011, A346962.

Sequence in context: A176443 A105225 A011018 * A156993 A308431 A292667

Adjacent sequences: A346960 A346961 A346962 * A346964 A346965 A346966

Keyword

nonn,cons

Author

Gleb Koloskov, Aug 09 2021

Status

approved