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%I #5 Mar 30 2012 18:58:15
%S 1,2,1,2,3,1,3,4,4,1,3,8,7,5,1,4,9,17,11,6,1,4,15,22,31,16,7,1,5,16,
%T 43,46,51,22,8,1,5,24,50,102,86,78,29,9,1,6,25,86,130,212,148,113,37,
%U 10,1,6,35,95,250,296,400,239,157,46,11,1,7,36,150,295,626,610
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209555; see the Formula section.
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+v(n-1,x),
%F v(n,x)=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 2...1
%e 2...3...1
%e 3...4...4...1
%e 3...8...7...5...1
%e First three polynomials v(n,x): 1, 2 + x , 2+ 3x + x^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];
%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[%] (* A209555 *)
%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[%] (* A209556 *)
%Y Cf. A209555, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 10 2012
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