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%I #20 Mar 18 2024 12:05:38
%S 0,1,18,207,2134,21465,214866,2149003,21490542,214906149,2149062490,
%T 21490626231,214906264038,2149062642577,21490626428514,
%U 214906264288515,2149062642889246,21490626428897373,214906264288979562,2149062642889802479,21490626428898032790
%N a(n) = 10*a(n-1)+n^3, a(0)=0.
%C a(n)/10^n converges to 470/2187=0.214906264...
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (14,-46,64,-41,10).
%F a(n) = (10^n-1)*(470/2187)-n^3/9-n^2*(10/27)-n*(110/243).
%F G.f.: -x*(x^2+4*x+1) / ((x-1)^4*(10*x-1)). - _Colin Barker_, Sep 13 2014
%t RecurrenceTable[{a[0]==0,a[n]==10a[n-1]+n^3},a,{n,20}] (* _Harvey P. Dale_, Mar 21 2023 *)
%o (PARI) concat(0, Vec(-x*(x^2+4*x+1)/((x-1)^4*(10*x-1)) + O(x^100))) \\ _Colin Barker_, Sep 13 2014
%Y Cf. A014824.
%K nonn,easy
%O 0,3
%A _Henry Bottomley_, Jul 04 2000
%E Corrected by _T. D. Noe_, Nov 08 2006
%E More terms from _Colin Barker_, Sep 13 2014
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