OFFSET
0,2
COMMENTS
Radius of convergence: r = (sqrt(17)-3)/16; A(r) = sqrt(2+6/sqrt(17)). Recurrence of A007482 is A007482(n) = 3*A007482(n-1) + 2*A007482(n-2). More generally, given {S} such that: S(n) = b*S(n-1) + c*S(n-2), |b|>0, |c|>0, then Sum_{n>=0} S(n)*Catalan(n)*x^n = sqrt( (1-2*b*x - sqrt(1-4*b*x-16*c*x^2))/(2*b^2+8*c) )/x.
FORMULA
G.f.: A(x) = sqrt((1-6*x - sqrt(1-12*x-32*x^2))/34 )/x.
n*(n+1)*a(n) -6*n*(2*n-1)*a(n-1) -8*(2*n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Nov 17 2018
EXAMPLE
Begins: {1*1, 3*1, 11*2, 39*5, 139*14, 495*42, 1763*132, 6279*429,...}.
PROG
(PARI) {a(n)=binomial(2*n, n)/(n+1)*((3+sqrt(17))^(n+1)-(3-sqrt(17))^(n+1))/2^(n+1)/sqrt(17)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2004
STATUS
approved