OFFSET
0,2
COMMENTS
In general, sum{k=0..n, sum{j=0..n, C(2(n-k),j)C(2k,j)r^j}} has expansion (1-(r+1)x)/((1+(r+3)x+(r-1)(r+3)x^2+(r-1)^3*x^3).
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,12,-8).
FORMULA
G.f.: (1-4x)/((1+2x)(1-8x+4x^2)); a(n)=6a(n-1)+12a(n-2)-8a(n-3); a(n)=sum{k=0..n, sum{j=0..n, C(2(n-k), j)C(2k, j)3^j}}.
a(0)=1, a(1)=2, a(2)=24, a(n)=6*a(n-1)+12*a(n-2)-8*a(n-3) [From Harvey P. Dale, Feb 21 2012]
a(n) = (-2)^n/2 +A102591(n)/2. - R. J. Mathar, Sep 20 2012
MATHEMATICA
CoefficientList[Series[(1-4x)/(1-6x-12x^2+8x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, 12, -8}, {1, 2, 24}, 30] (* Harvey P. Dale, Feb 21 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 04 2005
STATUS
approved