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A209574 Triangle of coefficients of polynomials v(n,x) jointly generated with A209573; see the Formula section.

%I A209574 #5 Mar 30 2012 18:58:15
%S A209574 1,2,3,3,7,5,4,14,20,7,5,24,52,45,9,6,37,110,155,86,11,7,53,203,403,
%T A209574 389,147,13,8,72,340,882,1240,856,232,15,9,94,530,1712,3204,3322,1702,
%U A209574 345,17,10,119,782,3040,7170,10088,7962,3125,490,19,11,147,1105
%N A209574 Triangle of coefficients of polynomials v(n,x) jointly generated with A209573; see the Formula section.
%C A209574 Combinatorial limit of row n satisfies linear recurrence
%C A209574 r(n)=4*r(n-1)-r(n-2) with r(1)=1 and r(2)=3.  For a
%C A209574 discussion and guide to related arrays, see A208510.
%F A209574 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209574 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209574 where u(1,x)=1, v(1,x)=1.
%e A209574 First five rows:
%e A209574 1
%e A209574 2...3
%e A209574 3...7....5
%e A209574 4...14...20...7
%e A209574 5...24...52...45...9
%e A209574 First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 5x^2.
%t A209574 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209574 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209574 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209574 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209574 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209574 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209574 TableForm[cu]
%t A209574 Flatten[%]   (* A209573 *)
%t A209574 Table[Expand[v[n, x]], {n, 1, z}]
%t A209574 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209574 TableForm[cv]
%t A209574 Flatten[%]   (* A209574 *)
%Y A209574 Cf. A209573, A208510.
%K A209574 nonn,tabl
%O A209574 1,2
%A A209574 _Clark Kimberling_, Mar 11 2012