%I #25 May 29 2025 13:01:09

%S 1,47,1634,50302,1449507,40067565,1076318788,28314922364,733113789893,

%T 18744640404523,474436263754662,11908153358721786,296798270974985959,

%U 7353307338085529321,181245852206166776456,4447409619636426706168,108701786686213403738505,2647602498778146844408359

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

%H Paolo Xausa, <a href="/A014941/b014941.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (47,-575,529).

%F G.f.: x/((1 - x)*(1 - 23*x)^2). - _Stefano Spezia_, Mar 11 2020

%F From _Elmo R. Oliveira_, May 22 2025: (Start)

%F E.g.f.: exp(x)*(1 + exp(22*x)*(506*x - 1))/484.

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

%F a(n) = 46*a(n-1) - 529*a(n-2) + 1 for n > 2.

%F a(n) = 47*a(n-1) - 575*a(n-2) + 529*a(n-3) for n >= 4. (End)

%t A014941[n_] := (23^n*(22*n - 1) + 1)/484; Array[A014941, 25] (* or *)

%t LinearRecurrence[{47, -575, 529}, {1, 47, 1634}, 25] (* _Paolo Xausa_, May 29 2025 *)

%o (PARI) a(n) = (1+23^n*(22*n-1))/484; \\ _Jinyuan Wang_, Mar 11 2020

%o (PARI) my(x='x+O('x^19)); Vec(-x/((x-1)*(23*x-1)^2)) \\ _Elmo R. Oliveira_, May 22 2025

%K nonn,easy

%O 1,2

%A _Olivier Gérard_

%E More terms from _Elmo R. Oliveira_, May 22 2025