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 A056578 #16 Apr 20 2025 12:33:13
%S A056578 1,10,49,142,313,586,985,1534,2257,3178,4321,5710,7369,9322,11593,
%T A056578 14206,17185,20554,24337,28558,33241,38410,44089,50302,57073,64426,
%U A056578 72385,80974,90217,100138,110761,122110,134209,147082,160753,175246,190585,206794,223897,241918
%N A056578 a(n) = 1 + 2*n + 3*n^2 + 4*n^3.
%H A056578 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A056578 a(n) = (A053699(n+1) - A053699(n-1))/2 - 4*n - 1.
%F A056578 G.f.: (1 + 6*x + 15*x^2 + 2*x^3)/(1-x)^4. - _Colin Barker_, Jan 10 2012
%F A056578 From _Elmo R. Oliveira_, Apr 20 2025: (Start)
%F A056578 E.g.f.: exp(x)*(1 + 9*x + 15*x^2 + 4*x^3).
%F A056578 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%e A056578 For n>4 this is 4321 translated from base n to base 10.
%t A056578 f[n_]:=1+2*n+3*n^2+4*n^3; lst={}; Do[AppendTo[lst,f[n]],{n,0,5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 12 2010 *)
%Y A056578 Note: 1 + 2*x + 3*x^2 + 4*x^3 is the first derivative of 1 + x + x^2 + x^3 + x^4, i.e., A053699.
%Y A056578 Cf. A000012, A005408, A056109, A056579.
%K A056578 easy,nonn
%O A056578 0,2
%A A056578 _Henry Bottomley_, Jun 29 2000
%E A056578 More terms from _Elmo R. Oliveira_, Apr 20 2025