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%I #15 Sep 08 2022 08:45:52
%S 1,2,-3,-75,-650,-4507,-28267,-167406,-955271,-5310911,-28962586,
%T -155616567,-826329687,-4345964510,-22675946635,-117526104883,
%U -605643805098,-3105646720979,-15856669574339,-80653146223054
%N Hankel transform of A105872.
%H G. C. Greubel, <a href="/A176290/b176290.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-27,10,-1).
%F G.f.: (1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2.
%p seq(coeff(series((1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2, x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Nov 25 2019
%t LinearRecurrence[{10,-27,10,-1},{1,2,-3,-75},30] (* _Harvey P. Dale_, Oct 29 2017 *)
%o (PARI) my(x='x+O('x^30)); Vec((1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2) \\ _G. C. Greubel_, Nov 25 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2 )); // _G. C. Greubel_, Nov 25 2019
%o (Sage)
%o def A176290_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2).list()
%o A176290_list(30) # _G. C. Greubel_, Nov 25 2019
%o (GAP) a:=[1,2,-3,-75];; for n in [5..30] do a[n]:=10*a[n-1]-27*a[n-2]+10*a[n-3] -a[n-4]; od; a; # _G. C. Greubel_, Nov 25 2019
%Y Cf. A105872.
%K easy,sign
%O 0,2
%A _Paul Barry_, Apr 14 2010