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 A221863 #21 Aug 06 2021 01:59:27
%S A221863 1,6,27,110,429,1637,6172,23104,86090,319792,1185305,4386331,16212913,
%T A221863 59873834,220964744,815057639,3005282745,11077802256,40824723483,
%U A221863 150424044413,554183037617,2041477665799,7519722443381,27696997721940,102010147865915,375697698147882
%N A221863 Expansion of (1-3*x+x^2)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
%C A221863 A diagonal of the square array A223968.
%H A221863 Michael De Vlieger, <a href="/A221863/b221863.txt">Table of n, a(n) for n = 0..1765</a>
%H A221863 László Németh and László Szalay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Nemeth/nemeth8.html">Sequences Involving Square Zig-Zag Shapes</a>, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
%H A221863 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-28,35,-15,1).
%F A221863 a(n) = A223968(n,n+4) = A223968(n,n+5).
%F A221863 G.f.: (1-3*x+x^2)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
%F A221863 a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5) with a(0) = 1, a(1) = 6, a(2) = 27, a(3) = 110, a(4) = 429.
%t A221863 CoefficientList[Series[(1-3x+x^2)/(1-9x+28x^2-35x^3+15x^4-x^5),{x,0,30}],x] (* or *) LinearRecurrence[{9,-28,35,-15,1},{1,6,27,110,429},30] (* _Harvey P. Dale_, Jan 26 2015 *)
%Y A221863 Cf. A223968
%K A221863 nonn,easy
%O A221863 0,2
%A A221863 _Philippe Deléham_, Apr 10 2013