|
|
A012340
|
|
exp(arcsin(x)*arcsin(x))=1+2/2!*x^2+20/4!*x^4+488/6!*x^6+22416/8!*x^8...
|
|
1
|
|
|
1, 2, 20, 488, 22416, 1680672, 187766592, 29343408768, 6124074217728, 1647634955248128, 555774895924564992, 229837057464353187840, 114397631096541960376320, 67482635629160164765409280
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ exp(Pi^2/4) * sqrt(Pi) * (2*n-1)! / sqrt(n). - Vaclav Kotesovec, Feb 08 2015
|
|
EXAMPLE
|
exp(arcsin(x)*arcsin(x)) = 1 + 2/2!*x^2 + 20/4!*x^4 + 488/6!*x^6 + 22416/8!*x^8 + ...
|
|
MATHEMATICA
|
nn = 20; Table[(CoefficientList[Series[E^(ArcSin[x]^2), {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *)
|
|
PROG
|
(PARI) x='x+O('x^50); v=Vec(serlaplace(exp(asin(x)*asin(x)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Apr 11 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Patrick Demichel (patrick.demichel(AT)hp.com)
|
|
STATUS
|
approved
|
|
|
|