OFFSET
0,2
COMMENTS
More generally, given {S} such that: S(n) = b*S(n-1) + c*S(n-2), |b|>0, |c|>0, S(0)=1, 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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..925
FORMULA
G.f.: sqrt( (1-4*x - sqrt(1-8*x-48*x^2))/32 )/x.
G.f.: sqrt( M(4*x) ), where M(x) is g.f. of A001006. - Werner Schulte, Aug 10 2015
Conjecture: n*(n+1)*a(n) -4*n*(2*n-1)*a(n-1) -12*(2*n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Oct 08 2016
G.f: B(m(4z)/4), where B(x) is the g.f. of A000984 and m(x) is the g.f. of A086246. - Alexander Burstein, May 20 2021
EXAMPLE
MATHEMATICA
CoefficientList[Series[Sqrt[(1 - 4*x - Sqrt[1 - 8*x - 48*x^2])/32]/x, {x, 0, 50}], x] (* G. C. Greubel, Jun 09 2017 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 26 2012
STATUS
approved