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 A156896 #13 Jan 07 2022 02:50:36
%S A156896 1,1,1,-1,0,1,1,-4,1,4,-2,0,1,1,-11,11,10,-22,3,11,-3,0,1,1,-26,66,0,
%T A156896 -131,78,62,-78,6,26,-4,0,1,1,-57,302,-245,-547,905,74,-901,342,292,
%U A156896 -228,10,57,-5,0,1,1,-120,1191,-2296,-1191,7128,-3572,-6648,7140,1216,-4749,1200,1171,-600,15,120,-6,0,1
%N A156896 Triangle formed by coefficients of the expansion of p(x, n), where p(x,n) = (1+x-x^3)^(n+1)*Sum_{j >= 0} (j+1)^n*(-x + x^3)^j.
%C A156896 Row sums are one.
%H A156896 G. C. Greubel, <a href="/A156896/b156896.txt">Rows n = 0..50 of the irregular triangle, flattened</a>
%F A156896 T(n, k) = coefficients of the expansion of p(x, n), where p(x,n) = (1+x-x^3)^(n + 1)*Sum_{j >= 0} (j+1)^n*(-x + x^3)^j.
%F A156896 T(n, 1) = (-1)*A000295(n) for n >= 2.
%e A156896 Irregular triangle begins as:
%e A156896 1;
%e A156896 1;
%e A156896 1, -1, 0, 1;
%e A156896 1, -4, 1, 4, -2, 0, 1;
%e A156896 1, -11, 11, 10, -22, 3, 11, -3, 0, 1;
%e A156896 1, -26, 66, 0, -131, 78, 62, -78, 6, 26, -4, 0, 1;
%e A156896 1, -57, 302, -245, -547, 905, 74, -901, 342, 292, -228, 10, 57, -5, 0, 1;
%t A156896 p[x_, n_] = (1+x-x^3)^(n+1)*Sum[(j+1)^n*(-x+x^3)^j, {j,0,Infinity}];
%t A156896 Table[CoefficientList[p[x, n], x], {n, 0, 10}]//Flatten
%o A156896 (Sage)
%o A156896 def T(n,k): return ( (1+x-x^3)^(n+1)*sum((j+1)^n*(x^3-x)^j for j in (0..3*n+1)) ).series(x, 3*n+3).list()[k]
%o A156896 flatten([1]+[[T(n,k) for k in (0..3*n-3)] for n in (1..12)]) # _G. C. Greubel_, Jan 06 2022
%Y A156896 Cf. A000295, A156890, A156901, A156918.
%K A156896 tabf,sign
%O A156896 0,8
%A A156896 _Roger L. Bagula_, Feb 17 2009
%E A156896 Edited by _G. C. Greubel_, Jan 06 2022