%I #4 Mar 30 2012 18:58:16
%S 1,1,3,1,5,5,1,5,15,7,1,5,19,35,9,1,5,19,63,69,11,1,5,19,71,177,121,
%T 13,1,5,19,71,249,429,195,15,1,5,19,71,265,781,923,295,17,1,5,19,71,
%U 265,957,2171,1807,425,19,1,5,19,71,265,989,3211,5407,3281,589,21
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210223; see the Formula section.
%C Limiting row: A001834
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...3
%e 1...5...5
%e 1...5...15...7
%e 1...5...19...35...9
%e First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 5x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t v[n_, x_] := 2 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[%] (* A210223 *)
%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[%] (* A210224 *)
%Y Cf. A210223, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 20 2012
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