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A013571
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Expansion of e.g.f. exp(arctan(x)/exp(x)).
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1
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1, 1, -1, -4, 9, 60, -175, -2154, 6433, 140984, -404063, -14300174, 38333361, 2070386084, -5007071823, -406148697538, 844312637249, 103808494182512, -173366392362431, -33528470038125974, 40208654504239441
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OFFSET
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0,4
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COMMENTS
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The inner function is arctan(x)/exp(x) = 2*x/2! - 6*x^2/2! + 4*x^3/3! + 20*x^4/4! + 54*x^5/5! - 770*x^6/6! - 2232*x^7/7! + ...
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..400
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EXAMPLE
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exp(arctan(x)/exp(x)) = 1 + x - 1/2!*x^2 - 4/3!*x^3 + 9/4!*x^4 + 60/5!*x^5 + ...
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MATHEMATICA
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Table[n!*SeriesCoefficient[Exp[ArcTan[x]/Exp[x]], {x, 0, n}], {n, 0, 50}] (* G. C. Greubel, Nov 19 2016 *)
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PROG
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(PARI) x='x + O('x^50); Vec(serlaplace(exp(atan(x)/exp(x)))) \\ G. C. Greubel, Nov 19 2016 *)
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CROSSREFS
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Sequence in context: A197997 A309444 A198178 * A002942 A028908 A265148
Adjacent sequences: A013568 A013569 A013570 * A013572 A013573 A013574
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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