%I #9 Sep 28 2020 02:03:34
%S -1,0,1,-3,11,-105,613,-12635,99677,-1774391,17582819,-1919343719,
%T 22882040099,-295793507053,1373607474819,-323119030735871,
%U 20600974525589671,-698062672818463097,12527062232269129201,-474730436062281169829,9471193365463611988187,-396898731474190849635703
%N Numerators of the coefficients in the expansion of li^{-1}(x)/x in powers of 1/LambertW(-1,-e/x).
%C li^{-1}(x) / x = Sum_{n>=-1} a(n)/A337735(n) * LambertW(-1,-e/x)^(-n).
%H Martin et al., <a href="https://mathoverflow.net/q/278626">Expansion of inverse logarithmic integral in terms of lambert w</a>, MathOverflow, 2017.
%F Function f(t) := Sum_{n>=1} a(n)/A337735(n) * t^{n-1} satisfies the differential equation: t^3*f'(t) + t*(1+2*t)*f(t) - (1+t)*log(1-t^2*f(t)) - t = 0 with f(0) = 1.
%p Order:=20: dsolve( { t^3*diff(f(t),t) + t*(1+2*t)*f(t) - (1+t)*log(1-t^2*f(t)) - t = 0, f(0)=1 }, f(t), series);
%Y Cf. A337735 (denominators).
%K frac,sign
%O -1,4
%A _Max Alekseyev_, Sep 17 2020