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 A260773 #20 Aug 19 2023 00:13:21
%S A260773 1,1,2,7,30,142,716,3771,20502,114194,648276,3737270,21819980,
%T A260773 128757020,766680856,4600866643,27797553638,168949310378,
%U A260773 1032267189636,6336728149794,39062959379620,241720286906116,1500910751651752,9348824475860702,58398701313158780
%N A260773 Certain directed lattice paths.
%C A260773 See Dziemianczuk (2014) for precise definition.
%H A260773 Lars Blomberg, <a href="/A260773/b260773.txt">Table of n, a(n) for n = 0..100</a>
%H A260773 M. Dziemianczuk, <a href="http://arxiv.org/abs/1410.5747">On Directed Lattice Paths With Additional Vertical Steps</a>, arXiv preprint arXiv:1410.5747 [math.CO], 2014.
%H A260773 M. Dziemianczuk, <a href="https://doi.org/10.1016/j.disc.2015.11.001">On Directed Lattice Paths With Additional Vertical Steps</a>, Discrete Mathematics, Volume 339, Issue 3, 6 March 2016, Pages 1116-1139.
%F A260773 G.f.: P2(x) = (1-x*P1(x))/(1-x-x*P1(x)), where P1(x) = 2*(1-x)/(3*x) - (2*sqrt(1-5*x-2*x^2)/(3*x))*sin(Pi/6 + arccos((20*x^3-6*x^2+15*x-2)/(2*(1-5*x-2*x^2)^(3/2)))/3). - See Dziemianczuk (2014), Proposition 11.
%F A260773 a(n) = A260771(n-1), n > 0 [see Proof of Proposition 11]. - _R. J. Mathar_, Aug 02 2015
%F A260773 a(n) = (1/n)*Sum_{j=0..floor((n-1)/4)} (-1)^j*C(n,j)*C(3*n-4*j-2,n-4*j-1), a(0)=1. - _Vladimir Kruchinin_, Apr 04 2019
%o A260773 (Maxima)
%o A260773 a(n):=if n=0 then 1 else sum((-1)^j*binomial(n,j)*binomial(3*n-4*j-2,n-4*j-1),j,0,floor((n-1)/4))/n; /* _Vladimir Kruchinin_, Apr 04 2019 */
%K A260773 nonn
%O A260773 0,3
%A A260773 _N. J. A. Sloane_, Jul 30 2015
%E A260773 More terms from _Lars Blomberg_, Aug 01 2015