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 A209359 #22 Mar 08 2023 18:01:44
%S A209359 0,1,33,357,2405,12405,53877,207541,731829,2411445,7531445,22523829,
%T A209359 64991157,181977013,496680885,1326120885,3473604533,8947236789,
%U A209359 22706651061,56869519285,140755599285,344683708341,835954147253,2009692372917,4792831180725,11346431180725
%N A209359 a(n) = 2^n * (n^4 - 4*n^3 + 18*n^2 - 52*n + 75) - 75.
%C A209359 This sequence is related to A036828 by the transform a(n) = n*A036828(n) - sum(A036828(i), i=0..n-1).
%H A209359 Bruno Berselli, <a href="/A209359/b209359.txt">Table of n, a(n) for n = 0..1000</a>
%H A209359 B. Berselli, A description of the transform in Comments lines: website <a href="http://www.lanostra-matematica.org/2008/12/sequenze-numeriche-e-procedimenti.html">Matem@ticamente</a> (in Italian).
%H A209359 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-50,120,-160,112,-32).
%F A209359 G.f.: x*(1+2*x)*(1+20*x+4*x^2)/((1-x)*(1-2*x)^5).
%F A209359 a(n) = (1/2) * Sum_{k=0..n} Sum_{i=0..n} k^4 * C(k,i). - _Wesley Ivan Hurt_, Sep 21 2017
%t A209359 LinearRecurrence[{11, -50, 120, -160, 112, -32}, {0, 1, 33, 357, 2405, 12405}, 26]
%t A209359 Table[2^n(n^4-4n^3+18n^2-52n+75)-75,{n,0,30}] (* _Harvey P. Dale_, Mar 08 2023 *)
%o A209359 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1+2*x)*(1+20*x+4*x^2)/((1-x)*(1-2*x)^5)));
%o A209359 (PARI) for(n=0, 25, print1(2^n*(n^4-4*n^3+18*n^2-52*n+75)-75", "));
%Y A209359 Cf. A000079, A000337, A036826, A036828.
%K A209359 nonn,easy
%O A209359 0,3
%A A209359 _Bruno Berselli_, Mar 07 2012