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 A165889 #7 Mar 10 2022 01:49:04
%S A165889 1,1,2,1,1,8,18,8,1,1,22,143,244,143,22,1,1,52,808,3484,5710,3484,808,
%T A165889 52,1,1,114,3853,35032,125746,188908,125746,35032,3853,114,1,1,240,
%U A165889 16782,290672,2000703,6040992,8702820,6040992,2000703,290672,16782,240,1
%N A165889 Irregular triangle T(n, k) = [x^k]( p(n, x) ), where p(n, x) = (1-x)^(2*n+4)*( Sum_{j >= 0} j^(n+1)*x^j )^2/x^2, read by rows.
%H A165889 G. C. Greubel, <a href="/A165889/b165889.txt">Rows n = 0..50 of the irregular triangle, flattened</a>
%F A165889 T(n, k) = [x^k]( p(n, x) ), where p(n, x) = (1-x)^(2*n+4)*( Sum_{j >= 0} j^(n+1)*x^j )^2/x^2.
%F A165889 T(n, k) = [x^k]( p(n, x) ), where p(n, x) = (1-x)^(2*n+4)*( PolyLog(-n-1, x)/x)^2.
%F A165889 T(n, n-k) = T(n, k). - _G. C. Greubel_, Mar 09 2022
%e A165889 Irregular triangle begins as:
%e A165889 1;
%e A165889 1, 2, 1;
%e A165889 1, 8, 18, 8, 1;
%e A165889 1, 22, 143, 244, 143, 22, 1;
%e A165889 1, 52, 808, 3484, 5710, 3484, 808, 52, 1;
%e A165889 1, 114, 3853, 35032, 125746, 188908, 125746, 35032, 3853, 114, 1;
%t A165889 p[n_, x_]:= p[n, x]= (1/x^2)*(1-x)^(2*n+4)*Sum[k^(n+1)*x^k, {k, 0, Infinity}]^2;
%t A165889 Table[CoefficientList[p[n, x], x], {n,0,12}]//Flatten (* modified by _G. C. Greubel_, Mar 09 2022 *)
%o A165889 (Sage)
%o A165889 def p(n,x): return (1/x^2)*(1-x)^(2*n+4)*sum( j^(n+1)*x^j for j in (0..2*n+4) )^2
%o A165889 def T(n,k): return ( p(n,x) ).series(x, 2*n+1).list()[k]
%o A165889 flatten([[T(n,k) for k in (0..2*n)] for n in (0..12)])
%Y A165889 Cf. A165883, A165890, A165891.
%K A165889 nonn,tabf
%O A165889 0,3
%A A165889 _Roger L. Bagula_, Sep 29 2009
%E A165889 Edited by _G. C. Greubel_, Mar 09 2022