OFFSET
0,2
COMMENTS
Unsigned version of A193618.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: sqrt( C(2*x)/C(-2*x) ) where C(x) = 1 + x*C(x)^2 is the Catalan function (A000108).
G.f.: exp( Sum_{n>=1} binomial(4*n-2,2*n-1)/2 * (2*x)^(2*n-1)/(2*n-1) ).
G.f. satisfies: A(x)*A(-x) = 1.
a(n) ~ sqrt(sqrt(2)-1)*(1+sqrt(2)-(-1)^n) * 2^(3*n-2) / (sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 25 2014
EXAMPLE
G.f.: A(x) = 1 + 2*x + 2*x^2 + 28*x^3 + 54*x^4 + 860*x^5 + 2004*x^6 +...
MATHEMATICA
CoefficientList[Series[Sqrt[(1 + Sqrt[1 + 8*x])/(1 + Sqrt[1 - 8*x])], {x, 0, 20}], x] (* Vaclav Kotesovec, Aug 25 2014 *)
PROG
(PARI) {a(n)=polcoeff( sqrt((1+sqrt(1+8*x +O(x^(n+2))))/(1+sqrt(1-8*x +O(x^(n+2))))), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 24 2014
STATUS
approved