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A359738
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a(n) = [x^n] (2*x^4 + 2*x^3 + 2*x^2 + x + 1)/(x^2 + 1).
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1
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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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FORMULA
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Let B(x) = x/(1 - exp(-x)), the e.g.f. of the Bernoulli numbers with B(1) = 1/2.
a(n) = signum([x^n] B(x)^2)) = signum([x^n] z^2 / (exp(-z) - 1)^2).
a(n) = signum([x^n] (x + 1)*B(x) - x*B'(x)).
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MAPLE
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ogf := (2*z^4 + 2*z^3 + 2*z^2 + z + 1)/(z^2 + 1):
ser := series(ogf, z, 100): seq(coeff(ser, z, n), n = 0..74);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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