|
| |
|
|
A158111
|
|
E.g.f.: sm^-1(x) = Sum_{n>=0} a(n)*x^(3n+1)/(3n+1)!; a(n) = coefficient of x^(3n+1)/(3n+1)! in the Maclaurin expansion of the inverse of the Dixon elliptic function sm(x,0).
|
|
0
| |
|
|
1, 4, 400, 179200, 216832000, 552487936000, 2554704216064000, 19415752042086400000, 225960522265801523200000, 3818732826292045742080000000, 89923520593525093134499840000000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| sm(x) = sm(x,0) satisfies: Integral_{0}^{sm(x,0)} dy/(1-y^3)^(2/3) = x.
|
|
|
FORMULA
| a(n) = Product_{k=1..n} (3k-2)*(3k-1)^2 for n>0 with a(0)=1.
E.g.f.: Sum_{n>=0} a(n)*x^(3m)/(3m)! = 1/(1-x^3)^(2/3).
|
|
|
EXAMPLE
| E.g.f.: 1/(1-x^3)^(2/3) = 1 + 4*x^3/3! + 400*x^6/6! + 179200*x^9/9! +...
E.g.f.: sm^-1(x) = x + 4*x^4/4! + 400*x^7/7! + 179200*x^10/10! +...
sm(x) = x - 4*x^4/4! + 160*x^7/7! - 20800*x^10/10! + 6476800*x^13/13! +...
|
|
|
PROG
| (PARI) a(n)=prod(k=1, n, (3*k-2)*(3*k-1)^2)
|
|
|
CROSSREFS
| Cf. A104133, A004988.
Sequence in context: A116031 A115049 A202172 * A198709 A036771 A201980
Adjacent sequences: A158108 A158109 A158110 * A158112 A158113 A158114
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Mar 18 2009
|
| |
|
|
