OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(2(n-2k), n-2k)/(1-2(n-2k))*2^k.
Recurrence: n*a(n) +2*(-2*n+3)*a(n-1) -2*n*a(n-2) +4*(2*n-3)*a(n-3) = 0. - R. J. Mathar, Feb 20 2015
MAPLE
with(FormalPowerSeries): # requires Maple 2022
rec:=subs(n=n-1, FindRE(sqrt(1-4*x)/(1-2*x^2), x, r(n))); # yields Mathar's recurrence
a:=gfun:-rectoproc({rec, r(0)=1, r(1)=-2, r(2)=0}, r(n), remember);
seq(a(n), n=0..20); # Georg Fischer, Oct 28 2022
MATHEMATICA
CoefficientList[Series[Sqrt[1-4x]/(1-2x^2), {x, 0, 30}], x] (* Harvey P. Dale, Mar 31 2015 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Apr 24 2005
STATUS
approved