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 A005223 M0369 #24 Dec 26 2021 21:05:55
%S A005223 0,0,1,0,2,2,7,10,29,52,142,294,772,1732,4451,10482,26715,64908,
%T A005223 165194,409720,1044629,2627712,6721492,17079076,43853111,112273270,
%U A005223 289390434,745262022,1928015211,4988699442,12949776427,33638741110,87590340673
%N A005223 Number of Dyck paths of knight moves.
%D A005223 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005223 Harvey P. Dale, <a href="/A005223/b005223.txt">Table of n, a(n) for n = 0..1000</a>
%H A005223 J. Labelle and Y.-N. Yeh, <a href="http://dx.doi.org/10.1016/0166-218X(92)90286-J">Dyck paths of knight moves</a>, Discrete Applied Math., 24 (1989), 213-221.
%F A005223 G.f.=1-1/A, where A=(1+2z+sqrt(1-4z+4z^2-4z^4)-sqrt(2)*sqrt(1-4z^2-2z^4+(2z+1)sqrt(1-4z+4z^2-4z^4)))/[4z^2].
%F A005223 a(n) ~ (23*sqrt(2*(9-5*sqrt(3))) + sqrt(138*(7*sqrt(3)-3))) * (1+sqrt(3))^n / (184*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Mar 10 2014
%F A005223 A(x) = 1 - 1/A005220(x). - _Gheorghe Coserea_, Jan 16 2017
%t A005223 CoefficientList[Series[1-1/(((1+2z+Sqrt[1-4z+4z^2-4z^4])-Sqrt[2] Sqrt[ 1-4z^2-2z^4+(2z+1)Sqrt[1-4z+4z^2-4z^4]])/(4z^2)),{z,0,40}],z] (* _Harvey P. Dale_, Oct 11 2011 *)
%K A005223 nonn,easy,nice,walk
%O A005223 0,5
%A A005223 _N. J. A. Sloane_
%E A005223 More terms from _Emeric Deutsch_, Dec 17 2003