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 A092766 #30 Oct 23 2018 12:10:11
%S A092766 1,1,1,-1,1,-5,-5,1,-15,0,-175,1,-35,175,-1225,-12250,6125,1,-70,1155,
%T A092766 -9800,-67375,-1414875,4716250,2358125,1,-126,4725,-80850,242550,
%U A092766 -12733875,-202327125,3034906875,0,11802415625,1,-210,15015,-512050,7882875,-121396275,-1618617000,-24886236375,1933235679375,-6750981737500,35442654121875,177213270609375,-59071090203125
%N A092766 Triangle read by rows: coefficients of Yablonskii-Vorob'ev polynomials.
%C A092766 Row n contains 1 + floor(n*(n+1)/6) terms (A008748). - _Gheorghe Coserea_, Nov 10 2016
%H A092766 Gheorghe Coserea, <a href="/A092766/b092766.txt">Rows n = 0..44, flattened</a>
%H A092766 M. Kaneko and H. Ochiai, <a href="http://arXiv.org/abs/math.QA/0205178">On coefficients of Yablonskii-Vorob'ev polynomials</a>
%F A092766 T(n) = Sum {k = 0..A008748(n)-1} a(n,k) * x^(A000217(n) - 3*k), where T(n)*T(n-2) = x*T(n-1)^2 + T(n-1)*T(n-1)'' - T(n-1)'^2, with T(0) = 1, T(1) = x. - _Gheorghe Coserea_, Nov 10 2016
%e A092766 T(0) = 1,
%e A092766 T(1) = x,
%e A092766 T(2) = x^3 - 1,
%e A092766 T(3) = x^6 - 5*x^3 - 5,
%e A092766 T(4) = x^10 - 15*x^7 - 175*x,
%e A092766 T(5) = x^15 - 35*x^12 + 175*x^9 - 1225*x^6 - 12250*x^3 + 6125,
%e A092766 ...
%e A092766 From _Gheorghe Coserea_, Nov 10 2016: (Start)
%e A092766 Triangle starts:
%e A092766 n\k [0] [1] [2] [3] [4] [5]
%e A092766 [0] 1;
%e A092766 [1] 1;
%e A092766 [2] 1, -1;
%e A092766 [3] 1, -5, -5;
%e A092766 [4] 1, -15, 0, -175;
%e A092766 [5] 1, -35, 175, -1225, -12250, 6125;
%e A092766 ...
%e A092766 (End)
%t A092766 T[0][_] = 1; T[1][x_] := x; T[n_][x_] := T[n][x] = (x T[n-1][x]^2 + T[n-1][x] T[n-1]''[x] - T[n-1]'[x]^2)/T[n-2][x] // Simplify;
%t A092766 row[n_] := Join[{1}, Partition[CoefficientList[T[n][x], x] // Reverse // Rest, 3][[All, 3]]];
%t A092766 Table[row[n], {n, 0, 8}] // Flatten (* _Jean-François Alcover_, Oct 23 2018 *)
%o A092766 (PARI) T(n)=if(n<2,if(n<1,n>=0,x),(x*T(n-1)^2+T(n-1)*T(n-1)''-T(n-1)'^2)/T(n-2))
%o A092766 (PARI)
%o A092766 seq(N) = {
%o A092766 my(x = 'x, t = vector(N));
%o A092766 t[1] = x; t[2] = x^3 - 1;
%o A092766 for (n = 3, N,
%o A092766 t[n] = (x*t[n-1]^2 + t[n-1]*t[n-1]'' - t[n-1]'^2)/t[n-2]);
%o A092766 concat(1, t);
%o A092766 };
%o A092766 pol2row(p) = {
%o A092766 my(tn = poldegree(p));
%o A092766 vector(1 + tn\3, k, polcoeff(p, tn-3*(k-1)));
%o A092766 };
%o A092766 concat(apply(pol2row, seq(8))) \\ _Gheorghe Coserea_, Nov 10 2016
%Y A092766 Cf. A000217, A008748, A177893.
%K A092766 sign,tabf
%O A092766 0,6
%A A092766 _Ralf Stephan_, Apr 23 2004
%E A092766 Offset corrected by _Gheorghe Coserea_, Nov 10 2016