This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A014938 #25 May 29 2025 13:01:46
%S A014938 1,43,1366,38410,1010815,25515421,625878268,15034586596,355440320845,
%T A014938 8298240786655,191776931546866,4395106938053518,100020864586079851,
%U A014938 2262634152933752305,50921433140756382520,1140878530467983299336,25460546264581733880793,566215511176052187986131
%N A014938 a(1)=1, a(n) = n*21^(n-1) + a(n-1).
%H A014938 Paolo Xausa, <a href="/A014938/b014938.txt">Table of n, a(n) for n = 1..500</a>
%H A014938 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (43,-483,441).
%F A014938 G.f.: x/((1 - x)*(1 - 21*x)^2). - _Stefano Spezia_, Mar 11 2020
%F A014938 From _Elmo R. Oliveira_, May 22 2025: (Start)
%F A014938 E.g.f.: exp(x)*(1 + exp(20*x)*(420*x - 1))/400.
%F A014938 a(n) = (21^n*(20*n - 1) + 1)/400.
%F A014938 a(n) = 42*a(n-1) - 441*a(n-2) + 1 for n > 2.
%F A014938 a(n) = 43*a(n-1) - 483*a(n-2) + 441*a(n-3) for n >= 4. (End)
%t A014938 A014938[n_] := (21^n*(20*n - 1) + 1)/400; Array[A014938, 25] (* or *)
%t A014938 LinearRecurrence[{43, -483, 441}, {1, 43, 1366}, 25] (* _Paolo Xausa_, May 29 2025 *)
%o A014938 (PARI) a(n) = (1+21^n*(20*n-1))/400; \\ _Jinyuan Wang_, Mar 11 2020
%o A014938 (PARI) my(x='x+O('x^19)); Vec(-x/((x-1)*(21*x-1)^2)) \\ _Elmo R. Oliveira_, May 22 2025
%K A014938 nonn,easy
%O A014938 1,2
%A A014938 _Olivier Gérard_
%E A014938 More terms from _Elmo R. Oliveira_, May 22 2025