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 A218744 #20 Aug 27 2024 21:47:23
%S A218744 0,1,42,1723,70644,2896405,118752606,4868856847,199623130728,
%T A218744 8184548359849,335566482753810,13758225792906211,564087257509154652,
%U A218744 23127577557875340733,948230679872888970054,38877457874788447772215,1593975772866326358660816,65353006687519380705093457
%N A218744 a(n) = (41^n - 1)/40.
%C A218744 Partial sums of powers of 41 (A009985).
%H A218744 Vincenzo Librandi, <a href="/A218744/b218744.txt">Table of n, a(n) for n = 0..600</a>
%H A218744 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218744 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (42,-41).
%F A218744 a(n) = floor(41^n/40).
%F A218744 G.f.: x/((1-x)*(1-41*x)). - _Vincenzo Librandi_, Nov 07 2012
%F A218744 a(n) = 42*a(n-1) - 41*a(n-2). - _Vincenzo Librandi_, Nov 07 2012
%F A218744 E.g.f.: exp(21*x)*sinh(20*x)/20. - _Elmo R. Oliveira_, Aug 27 2024
%t A218744 LinearRecurrence[{42, -41}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%o A218744 (PARI) A218744(n)=41^n\40
%o A218744 (Magma) [n le 2 select n-1 else 42*Self(n-1)-41*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218744 (Maxima) A218744(n):=(41^n-1)/40$
%o A218744 makelist(A218744(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218744 Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.
%Y A218744 Cf. A009985.
%K A218744 nonn,easy
%O A218744 0,3
%A A218744 _M. F. Hasler_, Nov 04 2012