login
A164111
Expansion of (1-x)/(1+4*x^2).
5
1, -1, -4, 4, 16, -16, -64, 64, 256, -256, -1024, 1024, 4096, -4096, -16384, 16384, 65536, -65536, -262144, 262144, 1048576, -1048576, -4194304, 4194304, 16777216, -16777216, -67108864, 67108864, 268435456, -268435456, -1073741824
OFFSET
0,3
COMMENTS
Hankel transform of 1,1,0,2,0,6,0,70,... (which has g.f. 1+x/sqrt(1-4x^2). See A126869).
FORMULA
a(n) = (-1)^C(n+1,2)*(4^(n/2)*(1+(-1)^n)/2 + 4^((n-1)/2)*(1-(-1)^n)/2).
a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011
MATHEMATICA
LinearRecurrence[{0, -4}, {1, -1}, 40] (* Harvey P. Dale, Sep 01 2015 *)
Rest[CoefficientList[Series[x*(1 - x)/(1 + 4*x^2), {x, 0, 50}], x]] (* G. C. Greubel, Sep 11 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((1-x)/(1+4*x^2)) \\ G. C. Greubel, Sep 11 2017
CROSSREFS
Sequence in context: A303072 A231839 A141125 * A056450 A164906 A213173
KEYWORD
easy,sign
AUTHOR
Paul Barry, Aug 10 2009
STATUS
approved