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 A165891 #10 Mar 10 2022 02:03:02
%S A165891 1,1,2,1,1,6,10,6,1,1,14,47,68,47,14,1,1,30,176,450,606,450,176,30,1,
%T A165891 1,62,597,2392,5162,6612,5162,2392,597,62,1,1,126,1926,11382,35967,
%U A165891 69132,85492,69132,35967,11382,1926,126,1,1,254,6043,50892,223785,600546,1060411,1277096,1060411,600546,223785,50892,6043,254,1
%N A165891 Irregular triangle T(n, k) = [x^k]( p(n, x) ), where p(n, x) = (1/x)*(1-x)^n*(1+x)^(n+2)*( Sum_{j >= 0} j^(n+1)*x^j ), read by rows.
%H A165891 G. C. Greubel, <a href="/A165891/b165891.txt">Rows n = 0..50 of the irregular triangle, flattened</a>
%F A165891 T(n, k) = [x^k]( p(n, x) ), where p(n, x) = (1/x)*(1-x)^n*(1+x)^(n+2)*( Sum_{j >= 0} j^(n+1)*x^j ).
%F A165891 T(n, k) = [x^k]( p(n, x) ), where p(n, x) = (1/x)*(1+x)^n * (1-x)^(n+2)*PolyLog(-n-1, x).
%F A165891 T(n, n-k) = T(n, k). - _G. C. Greubel_, Mar 09 2022
%e A165891 Irregular triangle begins as:
%e A165891 1;
%e A165891 1, 2, 1;
%e A165891 1, 6, 10, 6, 1;
%e A165891 1, 14, 47, 68, 47, 14, 1;
%e A165891 1, 30, 176, 450, 606, 450, 176, 30, 1;
%e A165891 1, 62, 597, 2392, 5162, 6612, 5162, 2392, 597, 62, 1;
%e A165891 1, 126, 1926, 11382, 35967, 69132, 85492, 69132, 35967, 11382, 1926, 126, 1;
%t A165891 p[n_, x_]:= p[n, x]= (1/x)*(1+x)^n*(1-x)^(n+2)*PolyLog[-n-1, x];
%t A165891 Table[CoefficientList[p[n, x], x], {n,0,12}]//Flatten (* modified by _G. C. Greubel_, Mar 09 2022 *)
%o A165891 (Sage)
%o A165891 def p(n,x): return (1/x)*(1+x)^n*(1-x)^(n+2)*polylog(-n-1, x)
%o A165891 def T(n,k): return ( p(n,x) ).series(x, 2*n+1).list()[k]
%o A165891 flatten([[T(n,k) for k in (0..2*n)] for n in (0..12)]) # _G. C. Greubel_, Mar 09 2022
%Y A165891 Cf. A158782, A165883, A165889, A165890.
%K A165891 nonn,tabf
%O A165891 0,3
%A A165891 _Roger L. Bagula_, Sep 29 2009
%E A165891 Edited by _G. C. Greubel_, Mar 09 2022