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 A078692 #18 Jul 14 2025 05:05:43
%S A078692 1,-2,-2,1,1,-4,0,10,0,-4,1,1,-6,6,19,-24,-24,19,6,-6,1,1,-8,16,20,
%T A078692 -80,-8,134,-8,-80,20,16,-8,1,1,-10,30,5,-160,128,330,-340,-340,330,
%U A078692 128,-160,5,30,-10,1,1,-12,48,-34,-240,468,399,-1416,-192,2020,-192,-1416,399,468,-240,-34,48,-12,1
%N A078692 Triangle reads by rows: T(n,k) = coefficient of x^k in (x^3-2*x^2-2*x+1)^n.
%C A078692 Original name: Coefficients of polynomials in the denominator of the generating function f(x)=(x-x^2)/(x^3-2x^2-2x+1) for F(n)^2 (where F(n) is the Fibonacci sequence) and its successive derivatives starting with the highest power of x.
%H A078692 Paolo Xausa, <a href="/A078692/b078692.txt">Table of n, a(n) for n = 1..11050</a> (rows 1..85 of triangle, flattened).
%F A078692 (d^(n)/d(x^n)) f(x), where f(x) = (x-x^2) / (x^3-2*x^2-2*x+1), for n=0, 1, 2, 3, ...
%e A078692 Triangle begins:
%e A078692 1, -2, -2, 1; # see A007598
%e A078692 1, -4, 0, 10, 0, -4, 1; # see A169630
%e A078692 1, -6, 6, 19, -24, -24, 19, 6, -6, 1;
%e A078692 ...
%t A078692 A078692row[n_] := Module[{x}, CoefficientList[(x^3 - 2*x^2 - 2*x + 1)^n, x]];
%t A078692 Array[A078692row, 6] (* _Paolo Xausa_, Jul 14 2025 *)
%o A078692 (PARI) row(n) = Vec((x^3-2*x^2-2*x+1)^n); \\ _Michel Marcus_, Jul 11 2025
%Y A078692 Cf. A007598, A169630.
%K A078692 sign,tabf
%O A078692 1,2
%A A078692 _Mohammad K. Azarian_, Feb 01 2003
%E A078692 Missing a(9) inserted and entry revised by _Sean A. Irvine_, Jul 11 2025