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%I #5 Mar 30 2012 18:58:15
%S 1,2,2,3,4,4,4,7,10,8,5,11,20,24,16,6,16,35,54,56,32,7,22,56,104,140,
%T 128,64,8,29,84,181,294,352,288,128,9,37,120,293,552,800,864,640,256,
%U 10,46,165,449,957,1610,2112,2080,1408,512,11,56,220,659,1562
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209697; see the Formula section.
%C 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 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...2
%e 3...4....4
%e 4...7....10...8
%e 5...11...20...24...16
%e First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 4x^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_] := x*u[n - 1, x] + (x + 1)*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[%] (* A209697 *)
%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[%] (* A209698 *)
%Y Cf. A209697, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 12 2012
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