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 A118981 #32 Feb 14 2022 00:18:37
%S A118981 1,1,1,1,2,3,1,3,6,4,1,4,10,12,7,1,5,15,25,25,11,1,6,21,44,60,48,18,1,
%T A118981 7,28,70,119,133,91,29,1,8,36,104,210,296,284,168,47,1,9,45,147,342,
%U A118981 576,699,585,306,76,1,10,55,200,525,1022,1485,1580,1175,550,123
%N A118981 Triangle read by rows: T(n,k) = abs( A104509(n-1,n-k) ).
%C A118981 The old definition was: "Companion Pell polynomials, as a triangle."
%H A118981 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lucas_polynomials">Lucas polynomials</a>.
%F A118981 For n >= 1, T(n,k) = Sum_{i=0..floor(k/2)} n/(n-i) * binomial(n-i,i) * binomial(n-2*i,n-k) = Sum_{i=0..floor(k/2)} (n/(n-i)) * binomial(k-i,i) * binomial(n-i,n-k). - _Max Alekseyev_, Oct 11 2021
%F A118981 G.f.: (1 + x^2)/(1-x-x^2 - x*y) (columns in reverse order). - _Georg Fischer_, Aug 13 2019
%F A118981 G.f. for row n >= 1 is the reciprocal of Lucas polynomial L_n(1+x). - _Max Alekseyev_, Oct 11 2021
%e A118981 First few rows of the triangle:
%e A118981 1;
%e A118981 1, 1;
%e A118981 1, 2, 3;
%e A118981 1, 3, 6, 4;
%e A118981 1, 4, 10, 12, 7;
%e A118981 1, 5, 15, 25, 25, 11;
%e A118981 ...
%e A118981 Polynomials: (1), (x + 1), (x^2 + 2x + 3), (x^3 + 3x^2 + 6x + 4), ...
%e A118981 Row 3: (1, 2, 3); as (x^2 + 2x + 3) = f(x), (x=1,2,3,...) of column 3 of A309220: (6, 11, 18, 27, 38, 51,...). The latter sequence = binomial transform of row 3 of A118980: (6, 5, 2).
%t A118981 Flatten[Map[Reverse,CoefficientList[CoefficientList[Series[(1 + x^2)/(1-x-x^2 - x*y), {x,0,8}], x], y]]] (* _Georg Fischer_, Aug 13 2019 *)
%o A118981 (PARI) {T(n, k) = polcoeff(polcoeff((1 + x^2)/(1 - x - x^2 - x*y) + x*O(x^n), n), n-k)}; /* _Michael Somos_, Oct 10 2021 */
%o A118981 (PARI) { A118981(n,k) = if(n==0, k==0, sum(i=0,k\2, n/(n-i) * binomial(k-i,i) * binomial(n-i,n-k) )); } \\ _Max Alekseyev_, Oct 11 2021
%Y A118981 Cf. A118980, A104509, A309220.
%K A118981 nonn,tabl
%O A118981 1,5
%A A118981 _Gary W. Adamson_, May 07 2006
%E A118981 Edited by _N. J. A. Sloane_, Aug 12 2019, replacing old definition by explicit formula from _R. J. Mathar_, Oct 30 2011
%E A118981 a(22)-a(62) from _Georg Fischer_, Aug 13 2019
%E A118981 More terms from _Michel Marcus_, Oct 11 2021