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%I #9 Jan 01 2024 16:20:29
%S 1,3,7,15,28,45,55,21,-155,-696,-2051,-5013,-10745,-20373,-33284,
%T -42231,-21545,97821,474985,1434000,3555097,7708515,14793463,24572583,
%U 32243644,20069445,-60546521,-323012523,-1000943027,-2518246440,-5524212203,-10728548565,-18105751145,-24497821821
%N Expansion of (1-x^2)/(1-3x+x^2+3x^3+x^4).
%C Results from applying a Chebyshev transform after an inverse Catalan transform to 1/(1-3x). 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 (3,-1,-3,-1)
%F a(n)=3a(n-1)-a(n-2)-3a(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)3^(n-2k-j)}}.
%t LinearRecurrence[{3,-1,-3,-1},{1,3,7,15},34] (* _James C. McMahon_, Jan 01 2024 *)
%K easy,sign
%O 0,2
%A _Paul Barry_, Dec 04 2004
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