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 A281261 #29 Feb 18 2019 16:08:48
%S A281261 1,2,2,1,5,2,5,9,2,1,15,14,2,7,35,20,2,1,28,70,27,2,9,84,126,35,2,1,
%T A281261 45,210,210,44,2,11,165,462,330,54,2,1,66,495,924,495,65,2,13,286,
%U A281261 1287,1716,715,77,2,1,91,1001,3003,3003,1001,90,2,15,455,3003,6435,5005,1365,104,2,1,120,1820,8008,12870,8008,1820,119,2
%N A281261 Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.
%C A281261 Row n>1 contains floor((n+3)/2) terms.
%H A281261 Gheorghe Coserea, <a href="/A281261/b281261.txt">Rows n = 1..202, flattened</a>
%H A281261 F. Chapoton, F. Hivert, J.-C. Novelli, <a href="http://arxiv.org/abs/1307.0092">A set-operad of formal fractions and dendriform-like sub-operads</a>, arXiv preprint arXiv:1307.0092 [math.CO], 2013.
%F A281261 A(x;t) = Sum{n>=1} P_n(t)*x^n = x*((1-t)*x^3 + (t^2-2*t-1)*x^2 + (2*t-1)*x + 1)/((t-1)*x^3 + (3-t)*x^2 - 3*x + 1).
%F A281261 A278457(x;t) = serreverse(A(-x;t))(-x).
%F A281261 A151821(n) = P_n(1), A213667(n) = P_n(2).
%F A281261 P_n(t^2) = ((1+t)^(n+1) + (1-t)^(n+1))/2 - t^2 + 1, for n>1.
%e A281261 A(x;t) = x + (2*t+2)*x^2 + (t^2+5*t+2)*x^3 + (5*t^2+9*t+2)*x^4 + ...
%e A281261 Triangle starts:
%e A281261 n\k [1] [2] [3] [4] [5] [6] [7] [8]
%e A281261 [1] 1;
%e A281261 [2] 2, 2;
%e A281261 [3] 1, 5, 2;
%e A281261 [4] 5, 9, 2;
%e A281261 [5] 1, 15, 14, 2;
%e A281261 [6] 7, 35, 20, 2;
%e A281261 [7] 1, 28, 70, 27, 2;
%e A281261 [8] 9, 84, 126, 35, 2;
%e A281261 [9] 1, 45, 210, 210, 44, 2;
%e A281261 [10] 11, 165, 462, 330, 54, 2;
%e A281261 [11] 1, 66, 495, 924, 495, 65, 2;
%e A281261 [12] 13, 286, 1287, 1716, 715, 77, 2;
%e A281261 [13] 1, 91, 1001, 3003, 3003, 1001, 90, 2;
%e A281261 [14] 15, 455, 3003, 6435, 5005, 1365, 104, 2;
%e A281261 [15] ...
%t A281261 Reverse[CoefficientList[#, t]]& /@ CoefficientList[x*((1-t)*x^3 + (t^2 - 2*t - 1)*x^2 + (2*t - 1)*x + 1)/((t-1)*x^3 + (3-t)*x^2 - 3*x + 1) + O[x]^16, x] // Rest // Flatten (* _Jean-François Alcover_, Feb 18 2019 *)
%o A281261 (PARI)
%o A281261 N=16; x='x+O('x^N); concat(apply(p->Vec(p), Vec(Ser(x*((1-t)*x^3 + (t^2-2*t-1)*x^2 + (2*t-1)*x + 1)/((t-1)*x^3 + (3-t)*x^2 - 3*x + 1)))))
%o A281261 (PARI)
%o A281261 N = 14; concat(1, concat(vector(N, n, Vec(substpol(((1+t)^(n+2) + (1-t)^(n+2))/2 - t^2 + 1, t^2, t)))))
%K A281261 nonn,tabf
%O A281261 1,2
%A A281261 _Gheorghe Coserea_, Jan 18 2017