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A014904 a(1)=1, a(n) = 20*a(n-1) + n.

%I A014904 #40 Mar 31 2025 16:58:29
%S A014904 1,22,443,8864,177285,3545706,70914127,1418282548,28365650969,
%T A014904 567313019390,11346260387811,226925207756232,4538504155124653,
%U A014904 90770083102493074,1815401662049861495,36308033240997229916,726160664819944598337,14523213296398891966758,290464265927977839335179
%N A014904 a(1)=1, a(n) = 20*a(n-1) + n.
%H A014904 Vincenzo Librandi, <a href="/A014904/b014904.txt">Table of n, a(n) for n = 1..200</a>
%H A014904 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (22,-41,20).
%F A014904 From _R. J. Mathar_, Jul 15 2010: (Start)
%F A014904 G.f.: x/((1-20*x)*(x-1)^2).
%F A014904 a(n) = 22*a(n-1) - 41*a(n-2) + 20*a(n-3). (End)
%F A014904 From _Elmo R. Oliveira_, Mar 31 2025: (Start)
%F A014904 E.g.f.: exp(x)*(20*exp(19*x) - 19*x - 20)/361.
%F A014904 a(n) = (20^(n+1) - 19*n - 20)/361. (End)
%t A014904 LinearRecurrence[{22, -41, 20}, {1, 22, 443}, 20] (* _Vincenzo Librandi_, Oct 20 2012 *)
%o A014904 (Magma) I:=[1, 22, 443]; [n le 3 select I[n] else 22*Self(n-1) - 41*Self(n-2) + 20*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2012
%o A014904 (Maxima)
%o A014904 a[1]:1$
%o A014904 a[2]:22$
%o A014904 a[3]:443$
%o A014904 a[n]:=22*a[n-1]-41*a[n-2]+20*a[n-3]$
%o A014904 A014904(n):=a[n]$
%o A014904 makelist(A014904(n),n,1,30); /* _Martin Ettl_, Nov 06 2012 */
%o A014904 (PARI) Vec(x/((1-20*x)*(x-1)^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jul 05 2024
%Y A014904 Row n=20 of A126885.
%K A014904 nonn,easy
%O A014904 1,2
%A A014904 _N. J. A. Sloane_, _Olivier Gérard_