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