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A058955
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Let S(t) = 1 + s_1*t + s_2*t^2 + ... satisfy S' = -S/(2 + S); sequence gives numerators of s_n.
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2
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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
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OFFSET
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0,7
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LINKS
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FORMULA
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S(t) = 2*LambertW((1/2)*exp(- (1/2)*t)*exp(1/2)).
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EXAMPLE
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S(t) = 1-1/3*t+1/27*t^2-1/4374*t^4-1/98415*t^5+...
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MAPLE
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t1 := diff(S(t), t) + S(t)/(2 + S(t)); dsolve({t1, S(0)=1}, S(t));
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MATHEMATICA
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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]];
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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