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

1, 1, -1, -4, 9, 60, -175, -2154, 6433, 140984, -404063, -14300174, 38333361, 2070386084, -5007071823, -406148697538, 844312637249, 103808494182512, -173366392362431, -33528470038125974, 40208654504239441

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: A197997 A309444 A198178 * A002942 A028908 A265148

Adjacent sequences: A013568 A013569 A013570 * A013572 A013573 A013574

Keyword

sign

Author

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

Status

approved