%I #10 Sep 08 2022 08:45:45

%S 0,0,0,0,1,1,-1,-4,-4,5,9,9,-14,-16,-16,30,25,25,-55,-36,-36,91,49,49,

%T -140,-64,-64,204,81,81,-285,-100,-100,385,121,121,-506,-144,-144,650,

%U 169,169,-819,-196,-196,1015,225,225,-1240,-256,-256

%N Hankel transform of A052702.

%C a(n+5) is the Hankel transform of A052702(n+4).

%H G. C. Greubel, <a href="/A160705/b160705.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-4,0,0,-6,0,0,-4,0,0,-1).

%F G.f.: x^4*(1-x)*(1+x+x^2)*(x^4+x^3-x^2+x+1)/( (1+x)^4*(x^2-x+1)^4 ).

%F a(n) = -4*a(n-3) -6*a(n-6) -4*a(n-9) -a(n-12).

%t LinearRecurrence[{0,0,-4,0,0,-6,0,0,-4,0,0,-1}, {0,0,0,0,1,1,-1,-4,-4,5,9,9}, 50] (* _G. C. Greubel_, May 02 2018 *)

%o (PARI) x='x+O('x^50); concat([0,0,0,0], Vec(x^4*(1-x)*(1+x+x^2)*(x^4+x^3-x^2+x+1)/( (1+x)^4*(x^2-x+1)^4 ))) \\ _G. C. Greubel_, May 02 2018

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0,0,0,0] cat Coefficients(R!(x^4*(1-x)*(1+x+x^2)*(x^4+x^3-x^2+x+1)/( (1+x)^4*(x^2-x+1)^4 ))); // _G. C. Greubel_, May 02 2018

%K easy,sign

%O 0,8

%A _Paul Barry_, May 24 2009