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A058955 Let S(t) = 1 + s_1*t + s_2*t^2 + ... satisfy S' = -S/(2 + S); sequence gives numerators of s_n. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Oct 01 2019 *)

CROSSREFS

Cf. A058956.

Sequence in context: A086738 A245803 A198941 * A176055 A072286 A007375

Adjacent sequences:  A058952 A058953 A058954 * A058956 A058957 A058958

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Jan 13 2001

STATUS

approved

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Last modified June 18 13:35 EDT 2021. Contains 345112 sequences. (Running on oeis4.)