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%I #7 Mar 30 2012 18:58:15
%S 1,2,2,1,6,4,1,4,16,8,1,3,16,40,16,1,3,11,56,96,32,1,3,10,43,176,224,
%T 64,1,3,10,35,163,512,512,128,1,3,10,34,128,579,1408,1152,256,1,3,10,
%U 34,117,477,1923,3712,2560,512,1,3,10,34
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A209691; see the Formula section.
%C Combinatorial limit of rows: A007052.
%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)=u(n-1,x)+2x*v(n-1,x)+1,
%F where u(1,x)=v(1,x)=1.
%e First five rows:
%e 1
%e 2...2
%e 1...6...4
%e 1...4...16...8
%e 1...3...16...40...16
%e First three polynomials v(n,x): 1, 2 + 2x , 1 + 6x + 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_] := u[n - 1, x] + 2 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[%] (* A209691 *)
%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[%] (* A209692 *)
%Y Cf. A209691, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 12 2012
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