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 A218728 #35 Aug 29 2024 02:11:53
%S A218728 0,1,26,651,16276,406901,10172526,254313151,6357828776,158945719401,
%T A218728 3973642985026,99341074625651,2483526865641276,62088171641031901,
%U A218728 1552204291025797526,38805107275644938151,970127681891123453776,24253192047278086344401,606329801181952158610026
%N A218728 a(n) = (25^n - 1)/24.
%C A218728 Partial sums of powers of 25 (A009969); q-integers for q=25.
%C A218728 Partial sums are in A014914. Also, the sequence is related to A014943 by A014943(n) = n*a(n) - Sum_{i=0..n-1} a(i) for n > 0. - _Bruno Berselli_, Nov 07 2012
%H A218728 Vincenzo Librandi, <a href="/A218728/b218728.txt">Table of n, a(n) for n = 0..700</a>
%H A218728 <a href="/index/Par#partial">Index entries related to partial sums</a>.
%H A218728 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (26,-25).
%F A218728 a(n) = floor(25^n/24).
%F A218728 From _Vincenzo Librandi_, Nov 07 2012: (Start)
%F A218728 G.f.: x/((1-x)*(1-25*x)).
%F A218728 a(n) = 26*a(n-1) - 25*a(n-2). (End)
%F A218728 E.g.f.: exp(13*x)*sinh(12*x)/12. - _Elmo R. Oliveira_, Aug 27 2024
%t A218728 LinearRecurrence[{26, -25}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 07 2012 *)
%t A218728 (25^Range[0,20]-1)/24 (* _Harvey P. Dale_, Aug 23 2020 *)
%o A218728 (PARI) A218728(n)=25^n\24
%o A218728 (Magma) [n le 2 select n-1 else 26*Self(n-1)-25*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 07 2012
%o A218728 (Maxima) A218728(n):=(25^n-1)/24$
%o A218728 makelist(A218728(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%Y A218728 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 A218728 Cf. A009969, A014914, A014943.
%K A218728 nonn,easy
%O A218728 0,3
%A A218728 _M. F. Hasler_, Nov 04 2012