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A009427
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Expansion of e.g.f. log(1+x)/cos(tan(x)).
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1
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0, 1, -1, 5, -12, 109, -405, 4913, -24976, 372633, -2419425, 42646845, -338219244, 6863821509, -64452230661, 1478191260393, -16062969072000, 410493211996977, -5072547848554017, 142840036992492789, -1979718755185227180
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) ~ (n-1)! * (-1)^(n+1) / cos(tan(1)) * (1 + tan(tan(1)) / ((cos(1))^2*n)). - Vaclav Kotesovec, Jan 27 2015
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MATHEMATICA
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With[{m=25}, CoefficientList[Series[Log[1+x]/Cos[Tan[x]], {x, 0, m}], x]*Range[0, m]!] (* modified by G. C. Greubel, Sep 06 2023 *)
CoefficientList[Series[Log[1 + x]*Sec[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)
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PROG
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(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cos(Tan(x)) ))); // G. C. Greubel, Sep 06 2023
(SageMath)
P.<x> = PowerSeriesRing(QQ, prec)
return P( log(1+x)/cos(tan(x)) ).egf_to_ogf().list()
(PARI) my(x='x+O('x^30)); concat([0], Vec(serlaplace(log(1+x)/cos(tan(x))))) \\ Joerg Arndt, Sep 06 2023
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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