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A013571 Expansion of e.g.f. exp(arctan(x)/exp(x)). 1
1, 1, -1, -4, 9, 60, -175, -2154, 6433, 140984, -404063, -14300174, 38333361, 2070386084, -5007071823, -406148697538, 844312637249, 103808494182512, -173366392362431, -33528470038125974, 40208654504239441 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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! + ...

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..400

EXAMPLE

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

MATHEMATICA

Table[n!*SeriesCoefficient[Exp[ArcTan[x]/Exp[x]], {x, 0, n}], {n, 0, 50}] (* G. C. Greubel, Nov 19 2016 *)

PROG

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

CROSSREFS

Sequence in context: A197859 A197997 A198178 * A002942 A028908 A265148

Adjacent sequences:  A013568 A013569 A013570 * A013572 A013573 A013574

KEYWORD

sign

AUTHOR

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

STATUS

approved

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Last modified December 7 14:52 EST 2016. Contains 278877 sequences.