OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..300
FORMULA
G.f.: A(x) = (1 - sqrt(1 - 4*x*(1-x)/(1-3*x+3*x^2) ))/2.
Recurrence: n*a(n) = 2*(5*n-6)*a(n-1) - (31*n-66)*a(n-2) + 42*(n-3)*a(n-3) - 21*(n-4)*a(n-4). - Vaclav Kotesovec, Oct 24 2012
a(n) ~ sqrt(14*sqrt(21)-42)*((7+sqrt(21))/2)^n/(16*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 24 2012
EXAMPLE
A(x) = x + 3*x^2 + 9*x^3 + 30*x^4 + 114*x^5 + 480*x^6 + 2157*x^7 +...
G(x) = x + x^2 + x^3 + 2*x^4 + 6*x^5 + 18*x^6 + 53*x^7 + 158*x^8 +...
where G(x) is the g.f. of A120010 and G(G(G(x))) = A(x).
MATHEMATICA
CoefficientList[Series[(1 - Sqrt[1 - 4 x (1-x) / (1 -3 x + 3 x^2)]) / x / 2, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)
PROG
(PARI) {a(n)=polcoeff((1 - sqrt(1 - 4*x*(1-x)/(1-3*x+3*x^2+x*O(x^n)) ))/2, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 14 2006
EXTENSIONS
Typo in Mma program fixed by Vincenzo Librandi, May 22 2013
STATUS
approved