%I #8 Oct 01 2019 19:55:26

%S 1,3,27,1,4374,98415,885735,3720087,55801305,1291401630,813583026900,

%T 4027235983155,724902476967900,7710326345931300,5343256157730390900,

%U 52845390570959910,5770716650348822172000,441459823751684896158000

%N Let S(t) = 1 + s_1*t + s_2*t^2 + ... satisfy S' = -S/(2 + S); sequence gives denominators 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+...

%t m = 17; 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]] // Denominator (* _Jean-François Alcover_, Oct 01 2019 *)

%Y Cf. A058955.

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_, Jan 13 2001