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%I #8 Aug 23 2021 15:54:14
%S 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,
%T 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,
%U 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
%N Decimal expansion of Integral_{x=-1/e..0} LambertW(x)*LambertW(-1,x) dx.
%F Equals Integral_{x=-1/e..0} LambertW(x)*LambertW(-1,x) dx.
%F Equals (3/e) - 1 + Sum_{n>0} (n^(n-1)/(n+1)^(n+2))*(Gamma(n+2,n+1)/Gamma(n+2)).
%F Equals (11/e)-4+Sum_{n>0} n^(n-1)/(n+1)^(n+2) = A135011-4+Sum_{n>0} A000169(n)/A007778(n+1).
%e 0.216577770436007277359024920060738331698735582255355693272331441694...
%p evalf(Integrate(LambertW(x)*LambertW(-1, x), x = -exp(-1)..0), 120); # _Vaclav Kotesovec_, Aug 23 2021
%t N[Integrate[LambertW[x]*LambertW[-1,x],{x,-1/E,0}],120]
%o (PARI) 11*exp(-1)-4+sumpos(n=1,(1/(1+1./n))^n/(n*(n+1)^2))
%Y Cf. A000169, A007778, A068985, A135003, A135011, A346962.
%K nonn,cons
%O 0,1
%A _Gleb Koloskov_, Aug 09 2021
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