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 A122766 #18 Jan 01 2023 02:57:55
%S A122766 2,-2,6,-6,-6,12,6,-24,-12,20,12,24,-60,-20,30,-12,60,60,-120,-30,42,
%T A122766 -20,-60,180,120,-210,-42,56,20,-120,-180,420,210,-336,-56,72,30,120,
%U A122766 -420,-420,840,336,-504,-72,90,-30,210,420,-1120,-840,1512,504,-720,-90,110
%N A122766 Triangle read by rows: let p(n, x) = x*p(n-1, x) - p(n-2, x), then T(n, x) = d^2/dx^2 (p(n, x)).
%H A122766 G. C. Greubel, <a href="/A122766/b122766.txt">Rows n = 1..50 of the triangle, flattened</a>
%H A122766 P. Steinbach, <a href="http://www.jstor.org/stable/2691048">Golden fields: a case for the heptagon</a>, Math. Mag. 70 (1997), no. 1, 22-31.
%F A122766 From _G. C. Greubel_, Dec 31 2022: (Start)
%F A122766 T(n, k) = 2*(-1)^binomial(n-k+1, 2)*binomial(k+1,2)*binomial(floor((n+k +2)/2), k+1).
%F A122766 T(n, 1) = 2*(-1)^binomial(n,2)*binomial(floor((n+3)/2), 2)
%F A122766 T(n, n) = 2*A000217(n).
%F A122766 Sum_{k=1..n} T(n, k) = 2*A104555(n).
%F A122766 Sum_{k=1..floor((n+1)/2)} T(n-k+1, k) = 2*([n=1] - [n=2]). (End)
%e A122766 Triangle begins as:
%e A122766 2;
%e A122766 -2, 6;
%e A122766 -6, 6, 12;
%e A122766 6, -24, -12, 20;
%e A122766 12, 24, -60, -20, 30;
%e A122766 12, 60, 60, -120, -30, 42;
%e A122766 -20, -60, 180, 120, -210, -42, 56;
%e A122766 20, -120, -180, 420, 210, -336, -56, 72;
%t A122766 (* First program *)
%t A122766 p[0, x]=1; p[1, x]=x-1; p[k_, x_]:= p[k, x]= x*p[k-1, x] -p[k-2, x]; b = Table[Expand[p[n,x]], {n,0,15}]; Table[CoefficientList[D[b[[n]], {x,2}], x], {n,2,14}]//Flatten
%t A122766 (* Second program *)
%t A122766 T[n_, k_]:= 2*(-1)^Binomial[n-k+1,2]*Binomial[k+1,2]*Binomial[Floor[(n +k+2)/2], k+1]; Table[T[n,k], {n,14}, {k,n}]//Flatten (* _G. C. Greubel_, Dec 31 2022 *)
%o A122766 (PARI) tpol(n) = if (n <= 0, 1, if (n == 1, x -1, x*tpol(n-1) - tpol(n-2)));
%o A122766 lista(nn) = {for(n=0, nn, pol = deriv(deriv(tpol(n))); for (k=0, poldegree(pol), print1(polcoeff(pol, k), ", ");););} \\ _Michel Marcus_, Feb 07 2014
%o A122766 (Magma)
%o A122766 A122766:= func< n,k | 2*(-1)^Binomial(n-k+1, 2)*Binomial(k+1,2)*Binomial(Floor((n+k+2)/2), k+1) >;
%o A122766 [A122766(n,k): k in [1..n], n in [1..14]]; // _G. C. Greubel_, Dec 31 2022
%o A122766 (SageMath)
%o A122766 def A122766(n, k): return 2*(-1)^binomial(n-k+1,2)*binomial(k+1,2)*binomial(((n+k+2)//2), k+1)
%o A122766 flatten([[A122766(n, k) for k in range(1, n+1)] for n in range(1, 15)]) # _G. C. Greubel_, Dec 31 2022
%Y A122766 Cf. A000217, A046854, A066170, A122765, A130777.
%K A122766 sign,tabl
%O A122766 1,1
%A A122766 _Roger L. Bagula_ and _Gary W. Adamson_, Sep 22 2006
%E A122766 Edited by _N. J. A. Sloane_, Oct 01 2006
%E A122766 Name corrected and more terms from _Michel Marcus_, Feb 07 2014