|
|
A012791
|
|
arctanh(sec(x)*arcsin(x))=x+6/3!*x^3+148/5!*x^5+9184/7!*x^7...
|
|
0
|
|
|
1, 6, 148, 9184, 1066640, 199000736, 54431471040, 20523724218880, 10203766053312768, 6467780044492713472, 5090997086675585360896, 4871968356294907783585792, 5570589015199967686042095616
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ (2*n)! / r^(2*n+1), where r = 0.6948196907307875655784200727751937626855... is the root of the equation sec(r)*arcsin(r) = 1. - Vaclav Kotesovec, Feb 05 2015
|
|
MATHEMATICA
|
nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x]*Sec[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 05 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Patrick Demichel (patrick.demichel(AT)hp.com)
|
|
STATUS
|
approved
|
|
|
|