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A014907 a(1)=1, a(n) = 22*a(n-1) + n.

%I A014907 #36 Mar 31 2025 14:44:06
%S A014907 1,24,531,11686,257097,5656140,124435087,2737571922,60226582293,
%T A014907 1324984810456,29149665830043,641292648260958,14108438261741089,
%U A014907 310385641758303972,6828484118682687399,150226650611019122794,3304986313442420701485,72709698895733255432688,1599613375706131619519155
%N A014907 a(1)=1, a(n) = 22*a(n-1) + n.
%H A014907 Vincenzo Librandi, <a href="/A014907/b014907.txt">Table of n, a(n) for n = 1..200</a>
%H A014907 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (24,-45,22).
%F A014907 a(1)=1, a(2)=24, a(3)=531, a(n) = 24*a(n-1) - 45*a(n-2) + 22*a(n-3). - _Vincenzo Librandi_, Oct 19 2012
%F A014907 From _Elmo R. Oliveira_, Mar 29 2025: (Start)
%F A014907 G.f.: x/((1-22*x)*(x-1)^2).
%F A014907 E.g.f.: exp(x)*(22*exp(21*x) - 21*x - 22)/441.
%F A014907 a(n) = (22^(n+1) - 21*n - 22)/441. (End)
%t A014907 LinearRecurrence[{24, -45, 22}, {1, 24, 531}, 20] (* _Vincenzo Librandi_, Oct 19 2012 *)
%o A014907 (Magma) I:=[1, 24, 531]; [n le 3 select I[n] else 24*Self(n-1) - 45*Self(n-2) + 22*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 19 2012
%o A014907 (Maxima)
%o A014907 a[1]:1$
%o A014907 a[2]:24$
%o A014907 a[3]:531$
%o A014907 a[n]:=24*a[n-1]-45*a[n-2]+22*a[n-3]$
%o A014907 A014907(n):=a[n]$
%o A014907 makelist(A014907(n),n,1,30); /* _Martin Ettl_, Nov 06 2012 */
%Y A014907 Row n=22 of A126885.
%K A014907 nonn,easy
%O A014907 1,2
%A A014907 _N. J. A. Sloane_, _Olivier Gérard_