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%I #25 Apr 02 2024 11:38:53
%S 1,3,10,35,126,460,1690,6225,22950,84626,312019,1150208,4239225,
%T 15621426,57556155,212037241,781074572,2877011660,10596599460,
%U 39027676220,143735627861,529352597361,1949472483601,7179308057596,26438877143476,97364252272077
%N Expansion of (1-3*x+x^2)^2/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
%C A diagonal of the square array A223968.
%H Colin Barker, <a href="/A216710/b216710.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-28,35,-15,1).
%F a(n) = A223968(n,n+1).
%F G.f.: (1-3*x+x^2)^2/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
%F a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5) with a(0) = 1, a(1) = 3, a(2) = 10, a(3) = 35, a(4) = 126.
%t CoefficientList[Series[(1 - 3 x + x^2)^2/(1 - 9 x + 28 x^2 - 35 x^3 + 15 x^4 - x^5), {x, 0, 25}], x] (* _Michael De Vlieger_, Aug 19 2015 *)
%t LinearRecurrence[{9, -28, 35, -15, 1},{1, 3, 10, 35, 126},26] (* _Ray Chandler_, Aug 28 2015 *)
%o (PARI) Vec((1-3*x+x^2)^2/(1-9*x+28*x^2-35*x^3+15*x^4-x^5) + O(x^30)) \\ _Colin Barker_, Aug 19 2015
%Y Cf. A223968.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Apr 09 2013