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%I #19 Aug 08 2019 18:50:10
%S 1,10,70,440,2675,16106,96720,580440,3482805,20897050,125382586,
%T 752295880,4513775735,27082654970,162495930500,974975583816,
%U 5849853503865,35099121024330,210594726147310,1263568356885400,7581410141314171
%N Expansion of 1/((1-x)^4*(1-6x)).
%C This sequence was chosen to illustrate a way to match generating functions and closed-form solutions.
%C The general term associated with the generating function
%C 1/((1-s*x)^4*(1-r*x)) with r>s>=1 is a(n) = [ r^(n+4) - s^(n+1)*(s^3 + s^2*(r-s)*binomial(n+4,1) + s*(r-s)^2*binomial(n+4,2)+(r-s)^3*binomial(n+4,3))]/(r-s)^4.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-30,40,-25,6).
%F a(n) = (6^(n+4) - (1 + 5*C(n+4,1) + 25*C(n+4,2) + 125*C(n+4,3)))/625 = (6^(n+5) - (125*n^3 + 1200*n^2 + 3805*n + 4026))/3750.
%e a(3) = (6^8 - (125*3^3 + 1200*3^2 + 3805*3 + 4026))/3750 = 440.
%Y Cf. A002663, A097786, A097788, A097790.
%K nonn,easy
%O 0,2
%A _Yahia Kahloune_, Sep 27 2013
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