OFFSET
0,3
COMMENTS
Hankel transform is A102591.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
FORMULA
G.f.: 1/((1+2x)*sqrt(1-4x)).
a(n) = Sum_{k=0..n} (-2)^(n-k)*C(2k,k).
Conjecture: n*a(n) + 2*(1-n)*a(n-1) + 4*(1-2n)*a(n-2) = 0. - R. J. Mathar, Nov 16 2011
a(n) = (-2)^n*JacobiP(n, 1/2, -1-n, -5). - Peter Luschny, Aug 02 2014
MATHEMATICA
Table[FullSimplify[(-2)^n/Sqrt[3] + 1/2*Binomial[2*(1+n), 1+n] * Hypergeometric2F1[1, 3/2+n, 2+n, -2]], {n, 0, 20}] (* Vaclav Kotesovec, Jan 31 2014 *)
CoefficientList[Series[1/((1 + 2*t)*Sqrt[1 - 4 t]), {t, 0, 50}], t] (* G. C. Greubel, Jun 13 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 04 2009
STATUS
approved