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%I #8 Feb 08 2020 20:40:53
%S 1,0,1,1,13,41,461,2745,32397,288937,3794605,44758649,665371565,
%T 9660560937,162652002189,2782536864697,52737562595917,
%U 1033546861769513,21867683869860845,481630083492884601,11277805333488014445,275314710164399079337,7077059249870048306125
%N E.g.f.: 1 / (2 - 1 / (2 + x - exp(x))).
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A032032(k) * a(n-k).
%F a(n) ~ n! * 2^(n-1) / ((c-1) * (2*c-3)^(n+1)), where c = -LambertW(-1, -exp(-3/2)) = 2.3576766739458990584... - _Vaclav Kotesovec_, Feb 08 2020
%t nmax = 22; CoefficientList[Series[1/(2 - 1/(2 + x - Exp[x])), {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) seq(n)={Vec(serlaplace(1/(2 - 1 / (2 + x - exp(x + O(x*x^n))))))} \\ _Andrew Howroyd_, Feb 08 2020
%Y Cf. A000670, A032032, A050351, A097236.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Feb 08 2020
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