%I #41 Mar 31 2025 12:40:56

%S 1,25,578,13298,305859,7034763,161799556,3721389796,85591965317,

%T 1968615202301,45278149652934,1041397442017494,23952141166402375,

%U 550899246827254639,12670682677026856712,291425701571617704392,6702791136147207201033,154164196131385765623777,3545776511021872609346890

%N a(1)=1, a(n) = 23*a(n-1) + n.

%H Vincenzo Librandi, <a href="/A014909/b014909.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (25,-47,23).

%F From _Harvey P. Dale_, Feb 05 2012: (Start)

%F a(1)=1, a(2)=25, a(3)=578, a(n) = 25*a(n-1) - 47*a(n-2) + 23*a(n-3).

%F G.f.: -x/((-1+x)^2*(-1+23*x)). (End)

%F From _Elmo R. Oliveira_, Mar 30 2025: (Start)

%F E.g.f.: exp(x)*(23*exp(22*x) - 22*x - 23)/484.

%F a(n) = (23^(n+1) - 22*n - 23)/484. (End)

%t Transpose[NestList[{First[#]+1,23Last[#]+First[#]+1}&,{1,1},20]][[2]] (* or *) LinearRecurrence[{25,-47,23},{1,25,578},20] (* _Harvey P. Dale_, Feb 05 2012 *)

%o (Magma) I:=[1, 25, 578]; [n le 3 select I[n] else 25*Self(n-1)-47*Self(n-2)+23*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Feb 05 2012

%Y Row n=23 of A126885.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, _Olivier Gérard_