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 A268329 #22 Jan 30 2020 21:29:17
%S A268329 2,10,40,150,550,2002,7280,26520,96900,355300,1307504,4828850,
%T A268329 17895150,66533250,248124000,927983760,3479939100,13082337900,
%U A268329 49295766000,186156379500,704415740028,2670587146260,10142836030240,38586876202000,147029304149000
%N A268329 Expansion of (1 - sqrt(1 - 4*x))^5/16.
%C A268329 a(n) is the number of North-East paths from (0,0) to (n,n) that cross the diagonal vertically exactly once and horizontally exactly twice, and bounce off the diagonal to the right once but not to the left. Details about this sequence can be found in Section 4.5 in Pan and Remmel's link. - _Ran Pan_, Feb 01 2016
%H A268329 Ran Pan, Jeffrey B. Remmel, <a href="http://arxiv.org/abs/1601.07988">Paired patterns in lattice paths</a>, arXiv:1601.07988 [math.CO], 2016.
%F A268329 G.f.: (1 - sqrt(1 - 4*x))^5/16.
%F A268329 a(n) = 10 * binomial(2n-6,n-5)/n.
%F A268329 a(n) = 2*A000344(n-3). - _R. J. Mathar_, Feb 17 2016
%F A268329 D-finite with recurrence: n*(n-5)*a(n) -2*(n-3)*(2*n-7)*a(n-1)=0. - _R. J. Mathar_, Feb 17 2016
%t A268329 Table[10 Binomial[2 n - 6, n - 5]/n, {n, 5, 29}] (* or *)
%t A268329 Table[SeriesCoefficient[(1 - Sqrt[1 - 4 x])^5/16, {x, 0, n}], {n, 5, 29}] (* _Michael De Vlieger_, Feb 17 2016 *)
%Y A268329 Cf. A000344, A000984.
%K A268329 nonn
%O A268329 5,1
%A A268329 _Ran Pan_, Feb 01 2016