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%I #28 Jul 02 2024 13:19:40
%S 1,5,10,45,95,415,890,3855,8305,35885,77410,334245,721295,3113815,
%T 6720290,29009655,62611105,270270485,583326010,2518004445,5434634495,
%U 23459291215,50632463690,218561383455,471723701905,2036254321085,4394872830610,18971017266645,40945381419695
%N Expansion of (1 + 5*x - 2*x^2 - 15*x^3) / (1 - 12*x^2 + 25*x^4).
%H Colin Barker, <a href="/A328605/b328605.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 (0,12,0,-25).
%F a(n) = 12*a(n-2) - 25*a(n-4) for n>3. - _Colin Barker_, Oct 21 2019
%F a(2*n)/a(2*n-1) ~ 2*a(2*n+1)/a(2*n) ~ 1 + sqrt(11).
%t CoefficientList[Series[(1+5x-2x^2-15x^3)/(1-12x^2+25x^4),{x,0,30}],x] (* or *) LinearRecurrence[ {0,12,0,-25},{1,5,10,45},30] (* _Harvey P. Dale_, Jul 02 2024 *)
%o (PARI) Vec((1 + 5*x - 2*x^2 - 15*x^3) / (1 - 12*x^2 + 25*x^4) + O(x^30)) \\ _Colin Barker_, Dec 13 2019
%Y Cf. A328604, A328606.
%K nonn,less,easy
%O 0,2
%A _Kyle MacLean Smith_, Oct 20 2019