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%I #8 Feb 08 2020 20:40:47
%S 1,0,1,1,10,31,271,1534,14603,120173,1310224,13947517,175477699,
%T 2265702388,32673218085,492565328493,8053045395018,138334722101571,
%U 2535114408394699,48790865853110950,991843960201311455,21121971129683138297,471959969940724275432
%N E.g.f.: 1 / (2 - exp(exp(x) - 1 - x)).
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000296(k) * a(n-k).
%F a(n) ~ n! * exp(1 - exp(c-1)/2) / ((1 - 2*exp(1-c)) * (c - 1 - log(2))^(n+1)), where c = -LambertW(-1, -exp(-1)/2) = 2.678346990016660653412884512094523... - _Vaclav Kotesovec_, Feb 08 2020
%t nmax = 22; CoefficientList[Series[1/(2 - Exp[Exp[x] - 1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) seq(n)={Vec(serlaplace(1/(2 - exp(exp(x + O(x*x^n)) - 1 - x))))} \\ _Andrew Howroyd_, Feb 08 2020
%Y Cf. A000296, A028248, A083355, A293037.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Feb 08 2020
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