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%I #10 Oct 01 2019 19:55:12
%S 1,-1,1,0,-1,-1,2,1,-1,-7,-37,368,4981,-9383,-1129837,461,27108469,
%T 68690009,-981587473,-23749507,31685207789,231197062,-394010311399,
%U -16467167272,-39133970611597,424044941703263,169016775569984281,-29438912370551
%N Let S(t) = 1 + s_1*t + s_2*t^2 + ... satisfy S' = -S/(2 + S); sequence gives numerators of s_n.
%F S(t) = 2*LambertW((1/2)*exp(- (1/2)*t)*exp(1/2)).
%e S(t) = 1-1/3*t+1/27*t^2-1/4374*t^4-1/98415*t^5+...
%p t1 := diff(S(t),t) + S(t)/(2 + S(t)); dsolve({t1, S(0)=1}, S(t));
%t m = 27; S[t_] = Sum[s[k] t^k, {k, 0, m}]; s[0] = 1;
%t sol = Solve[Thread[CoefficientList[S'[t] + S[t]/(2+S[t])+O[t]^m, t] == 0]];
%t s /@ Range[0, m] /. sol[[1]] // Numerator (* _Jean-François Alcover_, Oct 01 2019 *)
%Y Cf. A058956.
%K sign,frac
%O 0,7
%A _N. J. A. Sloane_, Jan 13 2001
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