|
Search: id:A088691
|
|
|
| A088691 |
|
E.g.f.: A(x) = f(x*A(x)^2), where f(x) = exp(atan(x)). |
|
+0
1
|
|
| 1, 1, 5, 47, 657, 12245, 285805, 8022555, 263276705, 9892965545, 418911700725, 19738761470375, 1024422336336625, 58067265415960125, 3569400983720767325, 236508279434832201875
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Radius of convergence of A(x): r = exp(-Pi/2) = 0.207879576..., with A(r) = exp(Pi/4) = 2.19328..., where r = limit a(n)/a(n+1)*(n+1) as n->infinity. Radius of convergence is from a general formula based on an heuristic argument.
|
|
FORMULA
|
a(n) equals the coefficient of x^n in (exp(atan(x)))^(2n+1)/(2n+1).
|
|
PROGRAM
|
(PARI) a(n)=n!*polcoeff((exp(atan(x)))^(2*n+1)+x*O(x^n), n, x)/(2*n+1)
|
|
CROSSREFS
|
Sequence in context: A058806 A006902 A127696 this_sequence A052802 A098799 A089155
Adjacent sequences: A088688 A088689 A088690 this_sequence A088692 A088693 A088694
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Oct 06 2003
|
|
|
Search completed in 0.002 seconds
|
