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 A192011 #38 Feb 15 2025 05:36:54
%S A192011 -1,2,0,2,0,1,2,0,-1,0,2,0,-3,0,-1,2,0,-5,0,0,0,2,0,-7,0,3,0,1,2,0,-9,
%T A192011 0,8,0,1,0,2,0,-11,0,15,0,-2,0,-1,2,0,-13,0,24,0,-10,0,-2,0,2,0,-15,0,
%U A192011 35,0,-25,0,0,0,1,2,0,-17,0,48,0,-49,0,10,0,3,0,2,0,-19,0,63,0,-84,0,35,0,3,0,-1
%N A192011 Let P(0,x) = -1, P(1,x) = 2*x, and P(n,x) = x*P(n-1,x) - P(n-2,x) for n > 1. This sequence is the triangle of polynomial coefficients in order of decreasing exponents.
%H A192011 G. C. Greubel, <a href="/A192011/b192011.txt">Rows n = 0..30 of triangle, flattened</a>
%F A192011 T(n, k) = T(n-1, k) - T(n-2, k-2), where T(0, 0) = -1, T(n, 0) = 2 and 0 <= k <= n, n >= 0. - _G. C. Greubel_, May 19 2019
%e A192011 The first few rows are
%e A192011 -1;
%e A192011 2, 0;
%e A192011 2, 0, 1;
%e A192011 2, 0, -1, 0;
%e A192011 2, 0, -3, 0, -1;
%e A192011 2, 0, -5, 0, 0, 0;
%e A192011 2, 0, -7, 0, 3, 0, 1;
%e A192011 2, 0, -9, 0, 8, 0, 1, 0;
%e A192011 2, 0, -11, 0, 15, 0, -2, 0, -1;
%e A192011 2, 0, -13, 0, 24, 0, -10, 0, -2, 0;
%e A192011 2, 0, -15, 0, 35, 0, -25, 0, 0, 0, 1;
%p A192011 A192011 := proc(n,k)
%p A192011 option remember;
%p A192011 if k>n or k <0 or n<0 then
%p A192011 0;
%p A192011 elif n= 0 then
%p A192011 -1;
%p A192011 elif k=0 then
%p A192011 2;
%p A192011 else
%p A192011 procname(n-1,k)-procname(n-2,k-2) ;
%p A192011 end if;
%p A192011 end proc: # _R. J. Mathar_, Nov 03 2011
%t A192011 p[0, _] = -1; p[1, x_] := 2x; p[n_, x_] := p[n, x] = x*p[n-1, x] - p[n-2, x]; row[n_] := CoefficientList[p[n, x], x]; Table[row[n] // Reverse, {n, 0, 9}] // Flatten (* _Jean-François Alcover_, Nov 26 2012 *)
%t A192011 T[n_,k_]:= If[k<0 || k>n, 0, If[n==0 && k==0, -1, If[k==0, 2, T[n-1,k] - T[n-2, k-2]]]]; Table[T[n,k], {n,0,10}, {k,0,n}]//Flatten (* _G. C. Greubel_, May 19 2019 *)
%o A192011 (PARI) {T(n,k) = if(k<0 || k>n, 0, if(n==0 && k==0, -1, if(k==0, 2, T(n-1,k) - T(n-2,k-2)))) };
%o A192011 for(n=0, 10, for(k=0, n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 19 2019
%o A192011 (Sage)
%o A192011 def T(n,k):
%o A192011 if (k<0 or k>n): return 0
%o A192011 elif (n==0 and k==0): return -1
%o A192011 elif (k==0): return 2
%o A192011 else: return T(n-1,k) - T(n-2, k-2)
%o A192011 [[T(n,k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, May 19 2019
%Y A192011 Left hand diagonals are: T(n,0) = [-1,2,2,2,2,2,...], T(n,2) = A165747(n), T(n,4) = A067998(n+1), T(n,6) = -A058373(n), T(n,8) = (-1)^(n+1) * A167387(n+2) (see also A052472(n)).
%K A192011 sign,easy,tabl
%O A192011 0,2
%A A192011 _Paul Curtz_, Jun 21 2011