A058955 Let S(t) = 1 + s_1*t + s_2*t^2 + ... satisfy S' = -S/(2 + S); sequence gives numerators of s_n.

1, -1, 1, 0, -1, -1, 2, 1, -1, -7, -37, 368, 4981, -9383, -1129837, 461, 27108469, 68690009, -981587473, -23749507, 31685207789, 231197062, -394010311399, -16467167272, -39133970611597, 424044941703263, 169016775569984281, -29438912370551

Offset

0,7

Links

Table of n, a(n) for n=0..27.

Formula

S(t) = 2*LambertW((1/2)*exp(- (1/2)*t)*exp(1/2)).

Example

S(t) = 1-1/3*t+1/27*t^2-1/4374*t^4-1/98415*t^5+...

Maple

t1 := diff(S(t), t) + S(t)/(2 + S(t)); dsolve({t1, S(0)=1}, S(t));

Mathematica

m = 27; S[t_] = Sum[s[k] t^k, {k, 0, m}]; s[0] = 1;
sol = Solve[Thread[CoefficientList[S'[t] + S[t]/(2+S[t])+O[t]^m, t] == 0]];
s /@ Range[0, m] /. sol[[1]] // Numerator (* Jean-François Alcover, Oct 01 2019 *)

Crossrefs

Cf. A058956.

Sequence in context: A351083 A245803 A198941 * A176055 A354986 A072286

Adjacent sequences: A058952 A058953 A058954 * A058956 A058957 A058958

Keyword

sign,frac

Author

N. J. A. Sloane, Jan 13 2001

Status

approved