OFFSET
0,2
COMMENTS
Partial sums of A006139. The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))g(x(1+x)).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f. : 1/((1-x)sqrt(1-4x-4x^2));
a(n)=sum{k=0..n, sum{i=0..n, C(k, i-k)}*C(2k, k)}.
Conjecture: n*a(n) +(2-5n)*a(n-1) +2*a(n-2)+4*(n-1)*a(n-3)=0. - R. J. Mathar, Dec 14 2011
a(n) ~ sqrt(34+23*sqrt(2))*(2+2*sqrt(2))^n/(7*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 17 2012
MATHEMATICA
CoefficientList[Series[1/((1-x)*Sqrt[1-4*x-4*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 17 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 16 2005
STATUS
approved