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A013571 Expansion of e.g.f. exp(arctan(x)/exp(x)). 1

%I

%S 1,1,-1,-4,9,60,-175,-2154,6433,140984,-404063,-14300174,38333361,

%T 2070386084,-5007071823,-406148697538,844312637249,103808494182512,

%U -173366392362431,-33528470038125974,40208654504239441

%N Expansion of e.g.f. exp(arctan(x)/exp(x)).

%C 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! + ...

%H G. C. Greubel, <a href="/A013571/b013571.txt">Table of n, a(n) for n = 0..400</a>

%e exp(arctan(x)/exp(x)) = 1 + x - 1/2!*x^2 - 4/3!*x^3 + 9/4!*x^4 + 60/5!*x^5 + ...

%t Table[n!*SeriesCoefficient[Exp[ArcTan[x]/Exp[x]], {x, 0, n}], {n,0,50}] (* _G. C. Greubel_, Nov 19 2016 *)

%o (PARI) x='x + O('x^50); Vec(serlaplace(exp(atan(x)/exp(x)))) \\ _G. C. Greubel_, Nov 19 2016 *)

%K sign

%O 0,4

%A Patrick Demichel (patrick.demichel(AT)hp.com)

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Last modified July 30 07:58 EDT 2021. Contains 346348 sequences. (Running on oeis4.)