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Expansion of (1-x^2)/(1-2x+2x^3+x^4).
0

%I #9 Jun 13 2015 00:51:37

%S 1,2,3,4,3,-2,-15,-40,-79,-126,-157,-116,99,638,1665,3248,5121,6274,

%T 4387,-4716,-27101,-69250,-133455,-207992,-250383,-164606,220227,

%U 1149212,2878019,5480190,8441729,9978208,6118017,-10127614,-48653373,-119520988,-224904765,-342375170

%N Expansion of (1-x^2)/(1-2x+2x^3+x^4).

%C Results from applying a Chebyshev transform after an inverse Catalan transform to 1/(1-2x). The inverse Catalan transform maps g(x)->g(x(1-x)) while the Chebyshev transform maps h(x)->(1/(1+x^2))h(x/(1+x^2)).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,-1)

%F a(n)=2a(n-1)-2a(n-3)-a(n-4); a(n)=sum{k=0..floor(n/2), sum{j=0..floor((n-2k)/2), C(n-k, k)C(n-2k-j, j)2^(n-2k-j)}}.

%t CoefficientList[Series[(1-x^2)/(1-2x+2x^3+x^4), {x,0,80}],x] (* _Harvey P. Dale_, Mar 14 2011 *)

%K easy,sign

%O 0,2

%A _Paul Barry_, Dec 04 2004