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 A081684 #14 Sep 12 2024 19:30:00
%S A081684 1,-1,-1,29,275,1829,10739,59429,318275,1670789,8656979,44454629,
%T A081684 226827875,1151991749,5830280819,29429454629,148249811075,
%U A081684 745630312709,3745590106259,18797445635429,94264432179875,472428649241669,2366562219717299,11850466059333029,59322887352366275,296896476647946629
%N A081684 a(n) = 5^n - 4^n - 3^n - 2^n + 3.
%C A081684 Inverse binomial transform of A081685.
%H A081684 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).
%F A081684 G.f.: (-1-254*x^4+266*x^3-99*x^2+16*x)/((x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
%F A081684 From _Elmo R. Oliveira_, Sep 12 2024: (Start)
%F A081684 E.g.f.: exp(x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3).
%F A081684 a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5) for n > 4. (End)
%t A081684 Table[5^n-4^n-3^n-2^n+3,{n,0,40}] (* _Harvey P. Dale_, Apr 01 2011 *)
%Y A081684 Cf. A081685.
%K A081684 easy,sign
%O A081684 0,4
%A A081684 _Paul Barry_, Mar 30 2003
%E A081684 a(24)-a(25) from _Elmo R. Oliveira_, Sep 12 2024