|
|
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
|
|
|
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) my(x='x + O('x^50)); Vec(serlaplace(exp(atan(x)/exp(x)))) \\ G. C. Greubel, Nov 19 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Patrick Demichel (patrick.demichel(AT)hp.com)
|
|
STATUS
|
approved
|
|
|
|