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 A209690 #8 Apr 05 2012 18:37:11
%S A209690 1,2,1,1,4,1,1,3,7,1,1,2,9,11,1,1,2,6,22,16,1,1,2,5,19,46,22,1,1,2,5,
%T A209690 14,54,86,29,1,1,2,5,13,42,135,148,37,1,1,2,5,13,35,124,302,239,46,1,
%U A209690 1,2,5,13,34,99,341,617,367,56,1,1,2,5,13,34,90,287,860,1171
%N A209690 Triangle of coefficients of polynomials v(n,x) jointly generated with A209689; see the Formula section.
%C A209690 Combinatorial limit of rows: odd-indexed Fibonacci numbers. For a discussion and guide to related arrays, see A208510.
%F A209690 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209690 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209690 v(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%e A209690 First five rows:
%e A209690 1
%e A209690 2...1
%e A209690 1...4...1
%e A209690 1...3...7...1
%e A209690 1...2...9...11...1
%e A209690 First three polynomials v(n,x): 1, 2 + x , 1 + 4x + x^2.
%t A209690 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209690 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209690 v[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
%t A209690 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209690 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209690 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209690 TableForm[cu]
%t A209690 Flatten[%] (* A209689 *)
%t A209690 Table[Expand[v[n, x]], {n, 1, z}]
%t A209690 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209690 TableForm[cv]
%t A209690 Flatten[%] (* A209690 *)
%Y A209690 Cf. A209689, A208510.
%K A209690 nonn,tabl
%O A209690 1,2
%A A209690 _Clark Kimberling_, Mar 12 2012