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A209760 Triangle of coefficients of polynomials v(n,x) jointly generated with A209759; see the Formula section.

%I A209760 #8 Mar 30 2012 18:58:15
%S A209760 1,1,3,1,3,8,1,3,11,21,1,3,11,38,55,1,3,11,41,124,144,1,3,11,41,150,
%T A209760 389,377,1,3,11,41,153,533,1187,987,1,3,11,41,153,568,1838,3549,2584,
%U A209760 1,3,11,41,153,571,2084,6168,10447,6765,1,3,11,41,153,571,2128
%N A209760 Triangle of coefficients of polynomials v(n,x) jointly generated with A209759; see the Formula section.
%C A209760 Limiting row: A001835
%C A209760 Coefficient of x^n in v(n,x):  even-indexed Fibonacci numbers
%C A209760 For a discussion and guide to related arrays, see A208510.
%F A209760 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209760 v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
%F A209760 where u(1,x)=1, v(1,x)=1.
%e A209760 First five rows:
%e A209760 1
%e A209760 1...3
%e A209760 1...3...8
%e A209760 1...3...11...21
%e A209760 1...3...11...38...55
%e A209760 First three polynomials v(n,x): 1, 1 + 3x , 1 + 3x + 8x^2.
%t A209760 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209760 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209760 v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209760 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209760 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209760 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209760 TableForm[cu]
%t A209760 Flatten[%]    (* A209759 *)
%t A209760 Table[Expand[v[n, x]], {n, 1, z}]
%t A209760 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209760 TableForm[cv]
%t A209760 Flatten[%]    (* A209760 *)
%Y A209760 Cf. A208510.
%K A209760 nonn,tabl
%O A209760 1,3
%A A209760 _Clark Kimberling_, Mar 14 2012