This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A229702 #19 Aug 08 2019 18:50:10 %S A229702 1,10,70,440,2675,16106,96720,580440,3482805,20897050,125382586, %T A229702 752295880,4513775735,27082654970,162495930500,974975583816, %U A229702 5849853503865,35099121024330,210594726147310,1263568356885400,7581410141314171 %N A229702 Expansion of 1/((1-x)^4*(1-6x)). %C A229702 This sequence was chosen to illustrate a way to match generating functions and closed-form solutions. %C A229702 The general term associated with the generating function %C A229702 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 A229702 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-30,40,-25,6). %F A229702 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 A229702 a(3) = (6^8 - (125*3^3 + 1200*3^2 + 3805*3 + 4026))/3750 = 440. %Y A229702 Cf. A002663, A097786, A097788, A097790. %K A229702 nonn,easy %O A229702 0,2 %A A229702 _Yahia Kahloune_, Sep 27 2013