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%I #23 Jan 01 2024 11:05:54
%S 1,-4,11,1,-284,2531,-15679,77836,-308549,831041,234356,-22885229,
%T 200108161,-1228842724,6056880491,-23790856319,62695694596,
%U 30510156611,-1841983774399,15815100054316,-96286306128869,471199253801921,-1833635630995564,4722739333912051
%N Expansion of (1 + 5*x)/(1 + 9*x + 25*x^2).
%C For positive n, a(n) equals the 5^n times the permanent of the (2n) X (2n) tridiagonal matrix with 1/sqrt(5)'s along the main diagonal, and i's along the superdiagonal and the subdiagonal (where i is the imaginary unit). - _John M. Campbell_, Jul 08 2011
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-9,-25).
%F G.f.: (1 + 5*x)/(1 + 9*x + 25*x^2).
%F a(n) = -9*a(n-1) - 25*a(n-2), a(0)=1, a(1)=-4.
%F a(n) = Sum_{k=0..n} binomial(n+k,2*k)*(-5)^(n-k).
%t CoefficientList[Series[(1 + 5x)/(25x^2 + 9x + 1), {x, 0, 25}], x]
%t LinearRecurrence[{-9,-25},{1,-4},30] (* _Harvey P. Dale_, Sep 10 2017 *)
%K easy,sign
%O 0,2
%A Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2003