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
Examples
0.216577770436007277359024920060738331698735582255355693272331441694...
Programs
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Maple
evalf(Integrate(LambertW(x)*LambertW(-1, x), x = -exp(-1)..0), 120); # Vaclav Kotesovec, Aug 23 2021
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Mathematica
N[Integrate[LambertW[x]*LambertW[-1,x],{x,-1/E,0}],120] -
PARI
11*exp(-1)-4+sumpos(n=1,(1/(1+1./n))^n/(n*(n+1)^2))