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A319116
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Signs of the Maclaurin coefficients of 1/(exp(x) + Pi/2).
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0
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1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1
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OFFSET
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0
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LINKS
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Table of n, a(n) for n=0..74.
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FORMULA
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Conjecture: a(n) is the same as the sign of cos((n+1)*arctan(Pi/log(Pi/2))). We can also use arctan(Pi/log(Pi/2))/Pi ~ 1/2 ~ 5/11 ~ 3776/8307 ~ 3781/8318 and so on. If the numerator is odd, we have, for example, a(n) = -a(n+2) or a(n) = -a(n+11) with some counterexamples. For even numerators we have, for example, a(n) = a(n+8307), also with some counterexamples.
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EXAMPLE
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a(1) = -a(12) = a(23) = -1.
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MAPLE
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S:= series(1/(exp(x)+Pi/2), x, 147):
seq(signum(coeff(S, x, j)), j=0..146);
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MATHEMATICA
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Sign[CoefficientList[Series[1/(Exp[x] + Pi/2), {x, 0, 100}], x]] (* G. C. Greubel, Oct 31 2018 *)
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PROG
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(PARI) apply(x->sign(x), Vec(1/(exp(x+O(x^100)) + Pi/2))) \\ Michel Marcus, Sep 13 2018
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CROSSREFS
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Cf. A210245, A210247.
Sequence in context: A210245 A210247 A256175 * A337004 A343785 A359738
Adjacent sequences: A319113 A319114 A319115 * A319117 A319118 A319119
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KEYWORD
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sign
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AUTHOR
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Mikhail Kurkov, Sep 10 2018
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STATUS
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approved
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