A106193 Expansion of sqrt(1-4x)/(1-2x^2).

1, -2, 0, -8, -10, -44, -104, -352, -1066, -3564, -11856, -40720, -141284, -497464, -1768368, -6343808, -22926426, -83402956, -305142432, -1122083312, -4144811244, -15372407464, -57222156528, -213709942208, -800563540356, -3007228179064, -11325019883616

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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

Cf. A106192.

Sequence in context: A097348 A271034 A185965 * A334875 A328476 A085814

Adjacent sequences: A106190 A106191 A106192 * A106194 A106195 A106196

Keyword

easy,sign

Author

Paul Barry, Apr 24 2005

Status

approved