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Expansion of e.g.f. log(1 - log(1 - x*exp(x))).
1

%I #10 Apr 03 2019 09:03:39

%S 0,1,2,4,17,123,1052,10568,125750,1726189,26730394,460982300,

%T 8766443952,182229703043,4110207945794,99970680376908,

%U 2608221938476016,72656914458625593,2152355976206481570,67562405794276542004,2240111797037473955984,78229640115171735522015,2870092624821982184377202

%N Expansion of e.g.f. log(1 - log(1 - x*exp(x))).

%p a:=series(log(1-log(1-x*exp(x))),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # _Paolo P. Lava_, Apr 03 2019

%t nmax = 22; CoefficientList[Series[Log[1 - Log[1 - x Exp[x]]], {x, 0, nmax}], x] Range[0, nmax]!

%o (PARI) my(x = 'x + O('x^30)); concat(0, Vec(serlaplace(log(1 - log(1 - x*exp(x)))))) \\ _Michel Marcus_, Mar 26 2019

%Y Cf. A007550, A009444, A089064, A307126.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 26 2019